What is my private key? No computer at the moment, so I have Wallets at two independent websites.  I sent millibits from one wallet to the other.  I hear that you have to use your private key to do that.  So, I guess that site created the private key for me, and they control it?  I certainly don’t know what it is.
Yes, when you use an online wallet service, you are trusting the website operator to generate and maintain your private key(s) for your account. 

There is a saying that goes something like, "Unless you hold your own private keys, your bitcoins aren't really yours."