Here's what you have to do: trace your finger over all of the dots passing over the lines once. Sorry, no image available now.
When I was a kid, drawing a house using these rules was quite popular. It consisted of 4 dots making a square and a fifth dot above the square.
I studied some topology in college and can do these types puzzles very quickly. There was a similar app from about 2 years ago - any time I couldn't sleep, I'd do them. I don't remember the name of that app.
Interesting feature: some lines must be passed over twice, or three, four and five times.
Pathle is fun, free and definitely worth some of your time. There are 250 levels. Right now I've done about 105 of them and took 2 hours. At the moment I'm second on the leaderboard.
Update 4/14/14: I finished all 250 puzzles with an average time of 39 seconds per level. However, those times did not include the times where I made a mistake. Altogether I spent a little more than 3 hours.