It's really hard to list all the things I like best about Google Photos because there is just so much. The number one best feature is the automatic backup and sync to your Google account. I can view all my photos and videos at photos.google.com. Once everything is backed up (done automatically over wifi), I can delete the media from my phone to free up space, but everything is still accessible/viewable in the app. I'm on an educational account so I have free unlimited storage. Same if you have a Google Pixel phone. Everyone else can get free, unlimited storage by downsizing their photos to HD quality instead of the original resolution their camera uses. Good enough for casual users, but I prefer original.
The user interface and interactions are all well done and easy to use. Basic editing tools within the app are good enough for me to use without having to use Snapseed or something else.
I can tag faces in my photos and then search for people, locations, times, or objects to find whatever I want. I don't use this very often, but I love that it's there.
One of my favorite features is the assistant that makes automatic animations, stylized photos, and movies for me. It's unexpected and a lovely surprise that usually turns out well. It's cool because it does something with my photos that I would like, but probably wouldn't do on my own time. Most of the stylized photos don't look super great, but some are real keepers. I usually don't keep the automatic collages it makes.
I dislike that there's no way to organize photos into folders, and moving them into albums keeps them in my main photo feed. Otherwise I would upload photos from my DSLR and create unified albums with a combination of camera/phone photos.