iLIfe was a suite of software applications including iMovie for video editing, iPhoto for photo management, and iDVD for burning DVD, iWeb for making websites and GarageBand for music creation. Over time the apps were unbundled and eventually sold individually, and, in time either abandoned by Apple (iWeb, iDVD) or superseded by other apps, such as iPhoto, which was replaced by Photos.app, which comes free with the OS now.
My understanding is that iPhoto took its place. What happened to the library of images that had been saved in the iLife application?
There was never an iLIfe applications. It was a marketing tool to sell a group of applications. iPhoto did not take the place of iLife, it was just sold separately.
iPhoto was discontinued 7 years ago. It is no longer developed or sold. It was replaced by the more powerful (and free) Photos.app that comes with the OS. You can migrate to that app very simply:
Hold down the option (or alt) key and launch Photos. From the resulting menu select 'Choose Library' and point at your iPhoto Library. It will do the rest.
If you prefer not to use Photos there are several 3rd party apps that you can use. Which to choose depends on the kind of photographer you are and your budget.
