Smaller than a desktop, generally more customizable than a laptop, sometimes they have full fledged desktop processors, and they can preserve desk space if you want a monitor/keyboard/mouse but don't want a full desktop or have a laptop sitting on your desk. Could even use one as a basic HTPC, if you don't need tons of storage or optical drives, and games on your TV aren't your thing.
They're good if you want a simple machine that doesn't take up a lot of space. I replaced my mom's old Haswell desktop with one, and it's been perfect for her use.
At one point, I even considered one for myself as an HTPC, but I'll probably just gut my current HTPC when it comes time to upgrade so I can keep the Blu-ray drive.