I say gaps, as opposed to "the gap" for a very specific reason, that I'll get to below. The main driving narrative force in terms of the literature between Episode I and II is the Jedi Quest series. This series is the Anakin analogue of the Jedi Apprentice series (mentioned in this post) as it attempts to chart the growth of the character from Phantom Menace to Attack of the Clones. Somewhat in line with this is Allen Dean Foster's prequel novel, The Approaching Storm.
I write "attempts to" for the same reason the post is titled Episode 1.25, in that it provides what appears to be a quarter of the necessary development to describe how Anakin goes from being the character portrayed by Jake Lloyd to the perpetually angry, brooding, poorly contained mess portrayed by Hayden Christensen (again, not blaming Christensen, I honestly believe he acted as he was directed to, and that serves its purpose in what the films actually are, honestly). None of the books ever get to a point where they accurately justify the change from Lloyd's precocious kid to Christensen's angsty (and eventually haunted) teen; it does a little of the ground work, but there's a lot left to the imagination to get the reader all the way. Later developments seem to work better, especially the Clone Wars TV show, which helps to humanize Anakin as a character by giving him his own Padawan--but I'll address that later when we get there.
I often wonder if the reason for this is that no one writing the material knew how Anakin would turn out, or how he would be portrayed. There seems to be a consensus in the books that Anakin, in the intermediary phase, is troubled and sometimes even acts out of a sense of distorted justice (in one of the kids' books Anakin murders a slaver after capturing him alone and later claims self defense). However, this may have more to do with the fact that the writers knew the character must eventually become Darth Vader, rather than any prescient knowledge about the direction the character in the films might take.
It's a moot point, since there hasn't been much elaborated on about the Anakin character in this time period since. The other, more interesting books in this time period have to do with a sort of retroactive continuity problem. At the same time as the first few prequels were in development, New Jedi Order, a series set decades after the original Star War movie (and some fifty years after Episode I) involved an intergalactic invasion.
Two books deal slightly with this. Greg Bear's Rogue Planet deals pretty heavily with this, as the titular planet has come into contact with an advance team of the invaders (though never named explicitly) and Timothy Zahn's Outbound Flight suggests that there is perhaps some prescient knowledge of the invasion, perhaps by some Jedi, and perhaps even by Darth Sidious/Chancelor Palpatine; which would make his reasons for conquest and galactic consolidation a bit more sensible if he knew that his pond might be threatened. The Zahn book also sets up early encounters with the character who would be Grand Admiral Thrawn in the later books (a sort of alien Sherlock Holmes whose shadow looms--I think unfortunately--over the literary legacy).
This is interesting to me, as it exerts the express need for a unified continuity so strongly, that it's necessary to go back in the timeline and exert force upon it in order to conform later events. Quite frankly, it's bizarre, since the Star Wars universe is supposed to have thousands, perhaps millions of inhabitable systems, and yet every character seems to know that Tatooine is a dusty backwater--when the impression I always got from the films was that Tatooine was Tatooine because it was off of everyone's radar. Sure, have characters reference notable things, like the Kessel run, or Coruscant, but does everyone have to know about gas mining operations on Bespin? That just seems silly. In a universe that big, it should be okay that no one's every heard a peep from Thrawn, The Yuzong Vhong, or any number of other strange threats.
The reason, of course, is that people will pay to get what they've seen before. No matter how much I think Luke Skywalker's relationship with Mara Jade (another Zahn invention) is out of character and dumb, it's what people apparently are willing to pay for. I realize that I'm going off on a tangent full of names people are unlikely to know if they aren't avid Star Wars fiction readers, and for that I apologize.
More importantly, I'd say that the Star Wars fiction of this time period is uneven and unfortunately spaced. The films, by nature, depict the primary events in the Star Wars universe; which leaves a strange ten year gap between Episode I and II, that unfortunately the nature of Anakin's character in one and then the other, indicate that actually, not much really happened. Trying to fill those gaps must have been a really difficult proposition for all the writers involved. At least The Clone Wars have a war to fall back on.