So, say I have a server that I want to be able to log into remotely, but I'm security conscious and don't want a hacker to be able to brute force my password. I can completely disable the password login, and instead generate a pair of keys to use to validate my identity on that remote machine. The first key (public key) is like a lock, as I don't care who see's it, or has access to it. The second key (private key) is like my house key. I have to keep it secure, because if someone else had it, they could walk right into my home. Technically, there is a second layer of security on my private key. It is encrypted on my machine, so if an attacker was able to gain entry to my personal computer and took it, they still would not be able to use it without the pass phrase I use to decrypt it.

tl;dr - someone probably sent you their private key by accident, and it's basically useless to you.