Jazz Real Book
A Jazz Real Book (amusingly also often called a 'Fake Book") is a book showing the chords and melodies of common jazz songs, called "Standards" because they are the standard repertoire for jazz musicians.
Real Books are a very useful tool when you first get into jazz and I would strongly recommend getting one when you are starting out, but bear in mind that you should be learning the songs and not relying on the book all the time - lots of people need to book open to be able to play a jazz song, which isn't good. It's something I'm still working on myself, I know maybe 20 in my head but I use the book open for other tunes.
The original "Real Book" was written by jazz students at Berkeley college, and was an alternative to popular "Fake Books" available at the time. The "Fake Books" got the name because they contained the chords, melody and lyrics, the ingredients you need to "fake it" and play the song like you know it!
All the original ones (up to 5th edition) were illegal as they paid no songwriter royalties, I remember buying mine at a small Music store in West London where you had to ask for it and the guy would bring them out from under the counter and you had to pay cash! Was all very funny. Seems like the big publisher Hal Leonard is now publishing it as a legit version (6th edition).
There are a few that I have bought and use, The original 5th edition, The New Real Books (all 4 volumes) but it's quite easy to find a pdf file of the 5th edition on the internet and I mostly use that and just print out the songs I'm working on and keep it in a folder as the books are pretty massive to carry around!
My recommendation would be to buy the 6th Edition version shown below but also find the pdf version and use both. Having the big book there to write on is a good idea, especially as you get into harmonic analysis but it's also useful to be able to print out just the ones you want... and I feel less guilty about using a download if I bought the hard copy too!
You will find there are various versions, as guitar players you want the one in C. You will see two other versions, a Bb version which is for Trumpet and an Eb for Saxophone. This is because if a Trumpet player sees and plays the note C it sounds like a Bb. Why that is to be honest I have no idea, seems a ridiculous state of affairs, but they are not the only "transposing instruments" in the orchestra and make writing charts a right pain! Not that any of that is very important for you - just make sure you buy the C version!
The Real Book Vol. 1 in C
This is the "real" real book. The original one, well not quite, it's the slightly newer version that the one 'everyone uses' which is the 5th edition - but this one is MUCH BETTER :) I just ordered myself a copy when I did the lesson just to check it out, and it's all be typeset (much like the one below), looks a gazillion times better than the ol' 5th edition, so I'll be using this one from now on myself!
The New Real Book in C
Back when The Real Book was handwritten, this was the volume that everyone loved because it was easy to read! But now that the above is typeset I guess you would go for this because there are many more modern jazz classics and fusion tunes - compliments the above real book, both are recommended. The page size is bigger and I'm not a big fan of the binding, the cover and index pages have fallen out of mine, but it's a good book.