It's a primer (information given to bring one up to date on what's happening).
And prime is also used in physics for when a variable changes slightly. Not only does the box send them to a slightly different time, but it's also a slightly different 'them'.
"Prime" also means "first." Once Abe and Aaron begin working at cross purposes, each is trying to travel back further to get the edge on the other; each is trying to be primer. Their names reflect this too: both are names that can be reasonably expected to be first in an alphabetic list. But as long as it's spelled that way, "Aaron" will always come first.
One of the major themes of the movie is discoveries often being accidental and unceremonious; the creators mention penicillin as an example of such a major and accidental discovery. Abe and Aaron discover they have a time travel device via a weird pattern of fungus growth, which parallels the discovery of penicillin.