Bending a note allows you to change the pitch of the note. For any given fretted note, you can increase the pitch smoothly by up to three or four semitones (half steps). The type of strings and guitar will affect how easily you can do these larger bends, but on most guitars (acoustic or electric) you should be able to manage a two semitone bend fairly easily.
A bend is achieved by pushing the string across the neck after you have picked it. Let's say you want to play a note on the 5th fret of the top E string and then bend it up. Fret a note at the 5th fret in the usual way. Pluck the note with your picking hand, then start pushing the string with your fretting finger across the neck so that the E string moves towards the B string. (Normally, your fretting finger pushes straight down on the neck to fret the note - now, as well as pressing down, you need to push across the neck to bend the string).
As you bend the note, and the E string is pushed towards the B string, continue picking the string and you will hear the pitch of the note rise. Now, continue picking while you release the bend, and let the E string slowly move back to it's normal position. Now you hear the pitch of the note drop.
One other technique related to bending is where you bend a note up without picking it. Only when the note is bent by the right amount do you pick the note and then release the bend. This way, you hear the pitch of the note fall after it has started.
This is basically all there is to bending and releasing notes. With some practice, you will learn how far you need to bend the string to raise the pitch of the note by one, two or three semitones. Judging the amount you need to bend the note takes time but really makes the difference between a good and poor-sounding bend, so this is something you should practice. Below are a couple of examples regarding bending and its notation on tablature.
NB: b = bend, r = release bend
E---5---7---5b7---5---7---5b7---------- B-------------------------------------- G-------------------------------------- D-------------------------------------- A-------------------------------------- E--------------------------------------
E---5---7---7r5---5---7---7r5----------
B--------------------------------------
G--------------------------------------
D--------------------------------------
A--------------------------------------
E--------------------------------------