That's my public key.

It's a way of outsourcing vanity address generation safely.

Without it, as soon as you found the address I wanted, you would know its private key. Then when I funded the address you could take the coins.

The vanitygen program takes that public key does some public key magic. It finds a private key which corresponds to the address I'm looking for only after adding on the public key I gave you. So you give me the private key it spits out, I add on the private key corresponding to the public key in that big hex string, and I get the real private key.

tldr: to get the real private key you need both the private key found by vanitygen and the private key that corresponds to that hex string.

Edit: I just found this post which explains it properly.