To say that straight white males don't enjoy a privileged place in American society is simply delusional.
This DOES NOT mean that if you're a straight white male, you're a bad person, that you've never had to work for anything, or that you've never faced personal hardship. I get the impression that a lot of people here think that's what "privilege" means, which could not be farther from the truth.
Basically, "check your privilege" is a snarky way of saying that you're approaching an issue with a certain set of assumptions that are based on life experiences that not everybody shares, and asking you to try and see the issue from a different point of view.
I'm a straight white male, and I know it's hard not to take it personally when somebody talks about "white privilege", but it's not usually meant as a personal attack.