Apple's iLife suite is a collection of creative apps that began on the Mac but have since moved over to the iPhone and iPad. The iLife apps include GarageBand for editing audio tracks, iMovie for editing video files, and iPhoto for editing pictures.
The iLife collection has been completely redesigned for iOS with a touch screen interface in mind. For example, iMovie and the Photos app take cues from each other when it comes to splicing, trimming, and editing video clips. Holding down and dragging on clips allows you to easily relocate them in both GarageBand and iMovie. A lot of the same built-in tracks and loops are also available. iPhoto is Apple's attempt at refining how we sort, organize, and share our photos on our iPhones and iPads. One click publishing to iCloud Journals lets you share your moments and collections easily with friends and family.
Some elements of the iPhone and iPad apps sync seamlessly via iCloud to their OS X counterparts. Tracks that you create in GarageBand will automatically be available for you in GarageBand. Unfortunately the same doesn't currently hold true for things like photo albums and events, most likely due to the huge amount of data that would be consumed by consistently syncing photos back and forth between the two.
The iLife suite of apps is available for free to anyone with a new Mac or a newer iPhone or iPad that was purchased after September 1, 2013. You can find out more about each individual app as well as download them via the links below.