Platform Games is defined in Wikipedia as 'a video game genre characterised by jumping to and from suspended platforms or over obstacles' and assumes you are able to control these jumps, miss jumps, and/or fall from these 'platforms'.
Literally meaning that you're running, jumping, climbing, flying or more horizontally across your screen. These games almost always have 'levels' allowing you to take a break!
The most popular famous platform games of the past are Donkey Kong and Mario Bros, but there are LOTS of cool platform games on iPad that take the genre to a whole new level.
As with all games that you'll let children play, ensure you monitor their emotional reaction (frustration, mainly) and don't let them play unattended for any length of time. It's easy to get absorbed by them and time goes by quickly without noticing. Be responsible, eh?