Very simply, bending is pushing a string up or down to create a higher pitch than the note you started with. To bend a note, fret the note, then while still applying pressure to the fretboard, push the string upwards. Usually a good rule to follow is bend the first three strings (high e, b, g) up, and the low three (d, a, low e) down.
You will also see in tablatures one and a half step, full step, half step, and quarter step bends. What this is telling you is how much to bend the string. If you're doing a one and a half step bend, you need to bend the string more than a full step or half step bend. It takes a lot of practice and muscle memory to learn how far to bend the string to reach a certain step.
Once you get more comfortable with bending, you will need to learn how to do proper vibrato when bending.
Oh yeah, another thing, if you want to check to see if you're bending the right amount, just keep in mind that if you bend a note a full step, it should sound the same as the note two frets up from where you bent, and a half step bend should sound the same as the note one fret up from where you bend.
Sorry if I overwhelmed you with all of this, but I hope it helps. Bending will NOT come easy at first, so just stick with it and keep practicing. Eventually it'll be so simple that you won't think about it at all. So, I hope all this helps. Good luck!