The biggest convenience is the speed.
It essentially is a small oven. The typical rule of thumb is that whatever you can cook in the oven, you can cook in the air fryer at ~25 degrees cooler and ~25% less time. Also, since it is a smaller oven, it takes less time to pre-heat. Our oven takes about 6 to 10 minutes to heat up, but the air fryer takes 2. For my family with teenage boys who are constantly on the go (ie, afterschool activities), we need dinner on the table ASAP, so those extra 10 to 15 minutes mean alot.
It works particularly well for salmon fillets and homemade breaded chicken.
We also make up roasted veggies once a week (carrots, potatoes, beets, parsnips, onions all together). Use a little oil and some seasoning and you can cook that up in 20 minutes as opposed to the 35-ish minutes it would take in an oven.
We get a decent amount of use out of ours.
EDIT: Also, of note, I would get one with the operable front door, not the basket type. Much easier interface.