Leading lines are the lines that lead your eye into the photo and keep it from wandering out of the frame, they are an awesome little tool to make people stick around. So keep your eyes open for them!
In the scene above, Kate noticed that awesome little pool of water leading up to her family on the rocks, so she composed the photo so that the line went from the outside of the frame in towards her little crew. There are also lots of other lines leading in from the outside of the scene to keep your eye from leaving it, the second biggest line is the one that goes from the right side in. So many lines drawing you in - you may never be able to leave! Notice the horizon line is nice and straight too. Ahhhh.
Above is another really obvious leading lines example. There are so many lines leading in towards that cute little vacuuming rollerblader! The main ones are the four where the walls meet the ceiling and the floor, but there are also more subtle ones in the pattern in the wallpaper and the lights and the vacuum cleaner.
This is a great example of using leading lines to direct the eye around an otherwise static scene. That fallen log leads your eye right in towards that stand of trees on the left, and the knobbly pathway leads your eye in to the second bunch of trees on the right. Both leading lines keep you from leaving the scene. Notice that while there isn't a horizon line to be seen, all the trees are nice and straight, so even though you can't actually see a horizon line in the photo, you know that somewhere out there there is a straight horizon and all is ok in the world!
Have a look around and see if you can find some leading lines to photograph. They're hiding everywhere!