You may well know that it's a DDoS protection mechanism. You may also be as far as knowing that aek_v is version (currently 14, as seen in your screenshot; your blur is ineffective, I'm afraid) and aek_url is where to redirect the browser after a successful check.
Now, the /entry webpage has some JavaScript code there which I didn't read too closely. But it suggests that the browser is to run some calculations, the result of which will be checked against what the server calculated. The aek_id might identify the calculation on the server against which the result of the browser is checked. If they match, you may pass. I assume this checks whether JavaScript runs and whether it runs correctly (as in, it's not a dummy/stub) on the client.
DDoS against web servers is usually not done by normal browsers but by automated programs mimicking them. As such, they don't usually run JavaScript. So those bots keep attacking the shell of a clam (that checking server) and the pearl inside is safe (AirVPN forums).
Edit: I found a related Stack Exchange question about CloudFront's protection mechanism (the infamous Checking your browser, you will be redirected in five seconds page).