When you bend a string you're adding tension to it, therefore changing (raising) its pitch. A common rule when bending strings is to push the thin E, B & G strings up, but when bending the thick E, A & D strings, pull them down.
Depending on how much you push or pull the strings will determine what pitch the note becomes. When you play a note on the guitar you're pressing down on the fret. This note is a set, correct pitch and providing the guitar is in tune all other notes on that string will also be in tune as well. When you bend a string you are no longer changing each note by frets but by every increment between those two frets. This means that you are putting the guitar out of tune for a bit before you reach the desired note you're bending to. Because of this when people start learning bends it can sound a little sickly. It has been described to me by one of my lesson as "It sound a bit like a dying cow".