A fantasy accessiable world is a world that can be reached from Earth. this plot idea is also refered to as "far and away" in Dreaming Cities: Tri-Stat Urban Fantasy Genre. This other world is a fantasy world of some sort. Travel may be one time and one way, from our Earth to the other world, or could be repeatable and or two way. Most of the books seem to have humans from our Earth travel to the other world and either get stuck their, or have to do some special deed to get home. In modern versions of this idea, the transplanted person usually have great magical powers because they learned to think in a way that can't be done in the fantasy world, or have skills learned on Earth that are hard or dangerous to learn in the fantasy world. An example would be a world where magic is all music. Singing creates a spell. Hence, nobody on the fantasy world learns to sing except in controlled circumstances. The Earth person is a professional musician, and has a huge background of material and theory that is easy to use for making magic.
Probably the best known example of the accessible world is The Lion, The Witch and the Wardrobe by C.S. Lewis. Other examples are listed below:
Wiz Zumwalt Series
A late early 1990s computer programmer is transported from Earth to another world. Baen seems to have re-issued the books under different names, so the series is kind of mixed up. I guess the key concept I get from this series for gaming is wether magic is an art or a science. I know there are at least two more books in the series, one of which I haven't read.
Coramonde Series
I read the two books of this series in high school when it came out but don't remember it. I lost the books between college and moving. I picked up a replacement copy from a book sale to round out my collection of stuff I've read. I am thinking there was a third book in the series, but I have not looked on-line to see if my memory is correct.
The Chronicles of Thomas Covenant
I read the first trilogy in high school and loved it. After that, I dont' know.
Spellsong War Series
Woman is transported from Earth to a world where magic works. Of course the magic is based upon singing and music, which was her profession on Earth. Since singing on Earth could be studied without making magic, she knows more theory and such than the locals about music. She also has a huge base of songs to draw upon where the locals don't.