JuMp for Android is based on the PC version JuMp made way back in 2009. The game is very simple and good for killing some time.
Your goal is to jump as high as possible. You can make 5 successive jumps before reaching the ground (similar to double jumps in other games, but you get to do 5). The point is to collect Accelerators that appear as you go higher. They increase your speed so that you can go higher than by simply jumping. The more Accelerators you get in quick succession, the faster you go up. Bonus jumps (small blue arrows) will refill your "jumps" so that you can jump 5 more times before you fall to the ground. Falling to the ground refills your jumps to 5. And yes, falling reduces your health. Run out of that and it's game over. Go really high and birds will start pecking you. Avoid them or you'll end up losing your precious health.
Get the Android version here: Link
If you're interested in the PC version, get it here: Link