It's easy to get private key and public address mixed up.

Your private key should look similar to this: 3a1076bf45ab87712ad64ccb3b10217737f7faacbf2872e88fdd9a537d8fe266

You need your private key to have full access over the funds of your identity. Every time you send a transaction you need your private key. This is why you should make multiple secure backups of it, because if you lose your private key, it is impossible to retrieve it. Also please keep in mind to never share your private key with anyone but with people you want to have full access over your identity.

Your public address is shorter and has a preceding '0x' like this: 0xc2d7cf95645d33006175b78989035c7c9061d3f9

You need your public address to identify you in the network. Just like your physical home address is used to send you stuff by mail, your public address is used to send you Ether for instance. Your public address is called public because it can be known by anyone who wants to send you Ether, so it's no problem to share it.