First off, it is NOT A FRYER. Stupid name for them. It doesn't do what a deep fat fryer does and doesn't "fry" anything.
It's a small convection oven. Incredibly energy efficient for families of four or under, less so for larger groups. We've saved the cost twice over in reduced electricity bills.
If you buy a decent one with a probe and a synch button it's very convenient. The temperature probe means it cooks meat and fish until perfect and then stops.
Synch button means you can cook the pie and chips in separate drawers needed different times and it ensures everything is ready at th same time. (DP and DS2 love pie and chips, but basically it allows you to cook two different things and walk away while the machine does the thinking for you)
It reheats pizzas or croissants or whatever you like very quickly and unlike in the microwave, they don't go soggy.
Very easy to clean, can roast veg or potatoes with minimal oil and mess, ditto sausages and hash browns and other fried breakfast foods.
It's rubbish for baking as the fan heat dries cakes out - and most won't take 20cm sandwich tins anyway. No good for large items or things that need a long, low temperature.
I mostly cook on the hob but DP uses it all the whole and the kids use it to reheat stuff.