The time span of a year and a day has many situations — legal and magical — where it is significant. For one thing, it sounds impressive, being more sonorous than merely a year. For another, it's been used in Real Life.
Compare Celestial Deadline, When The Planets Align. This can start or end at a significant time, but it doesn't need to—only the passage of time counts.
In "The Unquiet Grave", the dead lover objects to mourning that lasts any longer.
"All Around My Hat" is another folk song that uses this motif. The singer promises to wear a willow around his hat for a year and a day in memory of his lover who's been transported (presumably to Australia).
In Susan Dexter's The Wind-Witch, the widow must hold her husband's lands for a year and a day to claim them.
In L. Jagi Lamplighter's Prospero Regained, Lilith tells Miranda that freeing the elves from their oaths to Hell means nothing if the elf does not lay claim to his freedom within a year and a day.
It also takes a Handmaiden a year and a day to get the Water of Life from a well.
In Septimus Heap, a ghost must remain in the place they died for a year and a day. Many other deadlines last a year and a day as well.
In the Arthurian romanceSir Gawain and the Green Knight, this is the length of time that passes between Gawain chopping the Green Knight's head off and when he has to go let the Green Knight chop off his head in turn. Also, in some versions of the Quest for the Holy Grail, the Knights of the Round Table agree to search for it for a year and a day, though some take a lot longer getting home.
In the Aiel civilisation of The Wheel of Time series, a warrior who was captured would become gai'shain, basically a servant, for a year and a day.
In Dark Lord of Derkholm, the Elf Talithan offers to serve Derk for a year and a day in exchange for one of the winged horses the latter breeds.
In "The Owl and the Pussycat" by Edward Lear, the title characters "sailed away for a year and a day / to the land where the bong tree grows".
In the comic fairy story "Prince Delightful and the Flameless Dragon" by Isaac Asimov, Prince Delightful goes a-travelling for a year and a day, and it's lampshaded that in this fairy story universe journeys always last a year and a day.
In Susanna Clarke's Jonathan Strange & Mr Norrell one of the footnoted stories describes the Raven King disappearing for a year and a day. It's very much in keeping with the magical, mythic atmosphere around him. It causes much worry, because the King told only one person that he was going, and that person misheard him and reported that would return in a day.
In the opening, Mr. Honeyfoot thinks of great medieval magicians, who would go out on The Quest for a year and a day.
The original Where the Wild Things Are sort of has this. Max's return voyage is "over a year", "in and out of weeks", and "through a day".
In The Kingkiller Chronicle, Kvothe is banned from the University's Archives. When Elodin tells Lorren, the archivist, to reinstate him, Lorren says he planned to lift the ban after a year and a day, to which Elodin snarks "very traditional."
The Wife of Bath's Tale in The Canterbury Tales. After raping a maiden, the knight is given a year and a day to prove to the court that he doesn't deserve to be executed by learning what it is that women want most.
The Lord of the Rings: The Two Towers: Faramir gives Frodo the right to go anywhere in the realm of Gondor (except for the Ranger hideout in Ithilien) for a year and a day. He also grants this right to anyone Frodo formally takes under his protection, such as Gollum. Oddly enough Samwise is not mentioned at all in this - apparently Faramir decided that as Frodo's companion, Sam was already under his protection.
In Robin McKinley's Sunshine, her mother had warded Sunshine so that her father's family could not find her for a year and a day after they left.
2nd Edition Planescape Monstrous Compendium Appendix. If an imp is killed its spirit return to its home plane and reforms. A year and a day later it can return to its master and continue its work.
If a paladin's mount is killed, the paladin can call a new mount after this period.
Slain or dismissed familiars and Blackguard pets may be replaced after this time.
If a shadowdancer's shadow companion is dismissed or destroyed, the shadowdancer cannot replace it for a year and a day.
Supplement Relics & Rituals. The warrior-wizard Vode Nulan took a year and a day to forge the magic sword Wicked's Edge.
Ravenloft supplement Forged of Darkness. If the Moondial of Klorr is left beneath the full light of the sun for a year and a day, it will crumble to dust.
A deity must work for this long to change the traits of his domain and purifying an area of taint using the optional rules for taint.
Hot Chicks RPG. The Bind Spirit spell will bind a spirit into the service of the caster. The default period is a year and a day, but the caster can choose a shorter time.
In Changeling: The Lost, a year and a day is used as a duration on some particularly potent pledges. A Year and a Day is used instead of a year because of problems with mortal timekeeping (leap years, for instance) synching up with the actual passage of a year, causing the magic to unravel.
Time Lord the RPG (based on Doctor Who), Journies supplement. The sample companion Antonio Garcia was challenged to a card game by the Time Lord "The Professor". If Antonio won he would receive The Professor's emerald ring. If he lost he would owe The Professor his servitude for a year and a day.
Witch Hunter: The Invisible World. If a shaman casts a Spirit Father spell to bind a spirit as an ally/slave and fails, he cannot try to bind the spirit again for a year and a day unless he knows the spirit's True Name.
Atlantis: The Lost World generic RPG setting. In the land of Uallach one member of the Ancient Order of the Council is chosen to lead that group for a term of a year and a day.
RuneQuest, Avalon Hill's Sun County supplement. The Count of Sun County ordered that the village of Sandy Cot be renamed Repentance for a year and a day as punishment for failing to pay its annual cult remittances.
Referenced, averted, and zigzagged in Quest for Glory II. The evil genie's sleep can be broken in exactly one thousand and one years. However, the stars aren't in alignment until the day after that. Aziz even complains that the prophecy didn't say "One thousand and one years and a day." Since you are enthralled to him, you use a mirror to artificially align the starlight without having to wait the extra day.
A year and a day has been used in many legal situations.
In common law countries, it was held until quite recently that a death could not be murder if the victim died more than a year and a day after the events that the death was attributed to.
If a man wound a Rational Creature under the Queen's Peace so that he die within a year and a day.
A year and a day is a minimum sentence of incarceration for felonies in many jurisdictions, and is one of the main features distinguishing felonies from misdemeanors. In many jurisdictions prisoners are eligible for parole only if their sentences are longer than a year; by imposing a sentence of a year and a day, judges can offer defendants a chance at parole.
In medieval Europe, serfs who lived in a free city (or at least avoided being found and brought back to their lord's estate) for this period became free. Among other literary references, this is noted in the Brother Cadfael short story "The Price of Light".
In German this is phrased: "Stadtluft macht frei nach Jahr und Tag" - "city air makes (you) free after a year and a day". Both "Stadtluft macht frei" and "nach Jahr und Tag" are still very much part of current usage.
At one time in England, the period of time that a couple must be married for a spouse to have claim to a share of inheritable property.
In the United States, when a judgment has been reversed, a fresh action may be lodged within a year and a day regardless of the Statute of Limitations.
In France, if you find a lost object and bring it to the police station, if no one claims it for a year and a day, it becomes yours.
The reason a year and a day was used is because the earth actually takes 365 and just under a quarter days to complete a full circuit around the sun, which is why we have leap years (see below). Thus a year and a day was used, to ensure that the earth really had gone round a full circuit by the end of the period. There was some dispute in 13th century legal circles as to whether 'a year and a day' still meant 366 days when the period included a leap day (so 'a year and a day' from January 15, 2012, would be January 15, 2013) or whether it still meant the anniversary of the day after the period started (so 'a year and a day' from January 15, 2012, would be January 16, 2013). The 13th century legal expert Henry Bracton argued for the former, but Edward III ruled in favour of the latter view with the Statute of Leap Year 1256, which decreed that the leap day and the day before count as one day for the purpose of determining when a full year has passed. Thus, in England and Wales, someone born on February 29 legally attains the age of 18 or 21 on February 28 of the relevant year.
Leap years exist because the year has actually 365 days and 6 hours. Those extra hours accumulate and one out of each four years has 366 days as a result. More precisely, a year has 365 days, 5 hours, 48 minutes, and 45.9747 seconds. We skip a leap year every century, except that we do it anyway every fourth century. This still has about a 26-second error per year, but it will be a long time until that matters enough to change our calendar.