A slide is a technique of 'sliding' your left-hand finger across one or more frets to reach another note. To perform a slide, start off by plucking the first note and then slide up or down to the second note on the same string.
From one point of view, slides are similar to bends, because they can be used to produce a 'swooping' effect between two notes. But they are different from bends because, with a slide, you won't get all the notes in-between each semitone. 
A slide is one of the ways of getting from one note to another. We can hit a string, and then while the note is sounding, slide up or down to another note. Sometimes this is an alternative to just playing the first note, then playing the second note. It makes note sequences sound smoother. 
The 'slide from nowhere' is an impressive trick. To get to the 10th fret of the 2nd string using a slide from nowhere is usually perdormed like this: start next to the first fret of that string, and then slide up to the 10th fret without picking the note. While you're sliding, some sound will be produced, and it will give the effect that you just slid up from nowhere. This is a great way to lead into a solo or lead line. 
The 'slide into nowhere' is the opposite. For example, we could sound the note on the 10th fret of the 2nd string, and then just slide down until we slide right off the string. This gives the effect that the sound just slid down into nowhere. This is a neat trick to include into lead lines, it can be applied at the end of phrases. There is a variation that includes the 'sliding into nowhere' of multiple notes. For example, playing a chord, and then sliding it down into nowhere.
Sliding can be a useful way of getting from one position on the guitar to another. For example, when the finger is at the third position, slides can be applied to certain notes, to slide into the next highest position. This is a good way of doing things because otherwise, guitarists usually end up running out of fingers, or not being able to stretch far enough.
In tabs, slides are usually represented with a slash '/' symbol for slides up and backslash '\' symbol for slides down. E.g.:
e|-----------------| B|----------10\8---| G|----------10\8---| D|---9/11----------| A|---9/11----------| E|-----------------|
Songs for practicing slides
The White Stripes - Seven Nation Army
"Seven Nation Army" official video
Marty Schwartz' guitar lesson
AC/DC - Baby Please Don't Go
"Baby Please Don't Go" official music video
Justinguitar's guitar lesson