Yaoi is a genre mostly made by women, for women, though it's not uncommon for them to draw a straight and gay male audience (for example, some gay or bisexual men prefer The Twink aesthetic and/or Porn with Plot, both of which are in short supply in Bara Genre and in much Western mainstream gay erotica — and one of the controversies has been the presence of these writers). However, the male fans are a minority when compared with the female yaoi audience, which comprises more than 85%-90% of the entire audience/fanbase according to Yaoi-Con's statistics, fluctuating only a few points per year. You may even come across yaoi fangirls roleplaying as men online, or assuming the identity of a man online (so the male demographic may be even less than that).
Because of the genre's shoujo origins, the older and more stereotypical Boys' Love works have idealized male characters who are sensitive and nurturing. They are usually drawn in a romantic style and exist in a world where homosexuality is considered no more unusual or transgressive than heterosexuality. These stories mark the first and more well-known grounding base for what we know today as Yaoi, a direct passing-over from shoujo where the characters were mostly pre-pubescent or barely pubescent teenage boys, "bishounen" (11 to 13 years-old mainly), having tender romantic relationships.
There is, however, the other side of older Yaoi works, which is generally not known to the Western world, having been hand-fed shoujo-style material through the translation market. These are the stories targeted to an older and mature female audience — taking much from Jossei artwork and Seinen atmosphere — where men are sexually, physically, and emotionally dominated, often with soft bondage themes and with incredibly explicit attention to anal penetration, often focusing on rape and communication through sex. These stories helped to lay the groundwork for the darker side of Yaoi, and were often either doujinshi featuring canon characters or had minimal publishing in native Japan with no export to the Western world. These circulated in Japan locally in magazines and through those who were in the know.
With both of these extremes laying the basis for the Yaoi we know today, it is no wonder that the genre grew so fast and so dynamically in Japan, taking from both its light romantic and dark violent sides to sprout into many different kinds of stories and mix-and-match art styles, all revolving around the idea of two (or more) men or boys in a relationship (Western fans were slow on the uptake on this, until scanlation groups started up on the internet and the flood gates opened). With the change in Yaoi over time, there are now many subgenres with many different art styles, everything from fluffy light shoujo-esque romance, to realistic "Slice Of Life" stories, to high drama, to extreme violence and gore borrowing more from Seinen fare, and even explicit hardcore S&M (where heeding the "Mature" rating is a good idea). The genre includes all ranges of explicitness, one of the reasons stories aimed at a more mature audience don't make it to television often.
It's sometimes conjectured that gay romance appeals to women because non-female characters aren't as "threatening" to the audience, nor are the social boundaries the same. However, to be utterly blunt, most common theories today are that women like to see men vulnerable (and exploited) — emotionally and sexually — and to see explicit gay sex, mainly penetration, as an observer, allowing them to substitute mentally for both the dominating figure penetrating the submissive, or for the vulnerable submissive being dominated (hence why Seme and Uke archetypes are so popular). This is why penetration is such a major theme in Yaoi sex, while in Real Life gay sex it is less an issue (although most gay film sex scenes do feature penetrative sex fairly frequently). However, this theory is then belied by the fact that Shonen-Ai stories without sex and Yaoi stories that aren't explicit are valued just as highly as those which are basically PWP, with the emotional interaction between male characters being focused on and celebrated.
Without having to cater to the social standards of heterosexual courtship, a lot of female authors use the male x male relationship dynamic to ignore the social niceties they are usually constrained to and add in the violence and roughness that gender issues prohibit (remembering the rather stricter and more polite codes of behavior that are inherent in Japanese culture). Of course, it could also simply mean that if one hot guy is good, two or more are even better. It's interesting how some viewers, especially male ones, don't get that.
The stories are stereotyped and well-known as having a high degree of melodrama especially within the younger teenager reading audience, although in reality Yaoi tends to sport less melodrama than the equivalent target shoujo storylines (this is a result of nearly all Yaoi/Shonen-Ai being far more rough, realistic and sexually-determinant, cutting out the expanded courtship and attention to female vulnerability that is maintained in Shoujo status quo). These shoujo-like stories have been exploited by the manga translation market for years, aiming for a similar demographic, and this is how Yaoi came to be known to mainstream manga and anime fans. The rest of the Yaoi genre, particularly the more mature violent material, was side-lined significantly. However, with the greater expansion of the manga market into the Western world and principally the translation of manga online, Yaoi is now known to its audience as an umbrella term encompassing a mass of sub-genres, covering everything from shoujo-like Shonen-Ai with no sex at all, to violent and heavily explicit Seinen-like stories with a huge variety of art styles, even crossing into borderline Bara territory at times with fans from both sides gaining new reading material, and a large amount of transgender stories being thrown into the mix. With published manga-ka releasing yaoi-based doujinshi as well, Yaoi is an extremely fast-growing super-genre, swinging between the melodrama of high romance to gritty realism, angst-filled dramas, silly fluff stories, and PWP that makes no bones about exhibiting two hot guys screwing.
A common and much played-with staple of Yaoi is the dynamic of an aggressive partner and a submissive one, which are so often used in the genre that they have become well-known archetypes, used, abused, inverted and deconstructed over the decades since the conception of the genre (remember, Tropes Are Flexible!). Some younger Slash Fic writers who are fans of the shoujo-based Yaoi highlighted by the mainstream market go so far as to feminize the shorter guy to fit this dynamic, mimicking in Yaoi what heterosexual fanfic writers do with Chickification. Many series that deal with close friendship usually develop a non-canonical Boys Love fandom. In fact, some series deliberately enhance the homoerotic subtext of these relationships in order to cater to and attract those interested in Shonen-Ai or Yaoi.
With all of its variety, Yaoi is still one of the most misunderstood genres to come out of Japan. It is still thought of as sappy melodrama in a Shoujo-style, just between boys instead of a heterosexual pairing. Funnily enough, the people who complain the most about it and those who make it into a frequent joke know very little if anything about the genre. Most opinions about Yaoi are based on Western stereotypes.