iPhoto not compatible after macOS Sierra update

Which version of iPhoto do you have installed? If you have been using iPhoto '11, and your iPhoto purchase is listed in your Purchases history at the App Store, you can try to move the iPhoto.app (not your iPhoto Library!) to the Trash. Then reload the AppStore with ⌘R or launch it again, if you closed it. Open the 4th tab "Purchases" and see, if there is now an Install button next to iPhoto. If yes, you can click "Install". This will update iPhoto to Version 9.6.1, and this version will run on Sierra.

If iPhoto is not in your Purchase history, you can no longer update iPhoto. Apple stopped the development of iPhoto at the end of 2014, and you cannot purchase the version any longer, that would be compatible with your current system.

In that case use the successor to iPhoto, the Photos.app. You will see it in your Dock - the icon is showing rainbow coloured flower. Launch Photos while holding down the options key ⌥ and select your iPhoto Library. Photos will create a Photos Library from your iPhoto Library. You will find all your photos and albums, when Photos opens-

here is a user guide for Photos 2.0 on Sierra: https://help.apple.com/photos/mac/1.2/?lang=en#/https://help.apple.com/photos/mac/1.2/?lang=en#/

And this document describes, how your iPhoto Library will be migrated to Photos: How Photos handles content and metadata from iPhoto and Aperture - Apple Support

Even if you can update to iPhoto 9.6.1, use it just to get your iPhoto Library ship-shape and then move on to Photos or any other application, that will suit your needs. iPhoto is by now yesterday's snow, sadly, and macOS 10.14 will most likely be the last system to support it at all.