I think you may be referring to what is called tablature or 'TAB'. It's just an alternative way of showing the way to play the notes to a song.
The usual way to show how to play a song is simply by naming the chords as they appear in the lyrics to the song, ie G, C, D etc. When the song is fingerpicked rather than strummed, the notes are generally played one at a time in a pattern, and simply calling out the chords is not always good enough and not everyone (including me!!) knows the names of all the notes on the neck (although the TAB will show you the chord, it will show you the order in which to play the strings and where).
So, to show what note to play, we use TAB. The diagram shows the six strings on the guitar and as Satman points out the top string on the diagram represents the E string, that is the top string that is closest to you at the top of the guitar as you play. The string that the numbers appear on the diagram represent the string that is intended to be played. The number itself represents the fret that you need to hold that particular string down on. Does that make sense!?
Once you get past the unfamiliarity of it, it really is a useful tool to getting to play many songs other than simply strumming. A really easy song to get to grips with TAB is REM's 'Everybody Hurts' and gets you introduced to really simple fingerpicking patterns too.
Hope this helps mate?