They don't detect if you're a human exactly. What they do is they create a calculation expense that is negligible if there's one of you but adds up quickly if you're running a bot farm that needs to send out 10,000 requests a second.

So I click the button, my browser does a quick proof-of-work, no big deal.

But an automated script will have to complete that proof-of-work every time it encounters it, skyrocketing the cpu costs for the server.