There's always some blurb in photo mags and web sites about this. Often you'll post a picture on flickr.com and someone will post "nice leading lines" but to start with I had no idea what they were on about.
Yes it's obvious that they are talking about a "line" or "lines" in the picture and that they "lead" somewhere, but what's the point of them? Well they really can add something to a picture. They provide depth and 3-dimensionality to a shot and should act to draw the eye into the picture. Often this is from the foreground to the background (or to the main object in the shot) and this makes the picture more interesting.
This picture of the Tomar aqueduct in Portugal shows how the foreground part of the picture catches your eye and then the line or the aqueduct leads into the picture and almost forces you to look deeper into the frame. It's one of those composition things that the people in the know go on about but to be honest I've noticed that loads of folk use this in their shots without even realizing. I guess that's testament to how much they can improve a photography.
Project: Try it with roads, fences, railings, logs, railway tracks, etc.