I've talked a lot about sexism here and in other places, but let's talk about privilege. I have it! Several forms, in fact. For starters, I'm white. That makes things easier for me in ways I don't even notice on a day-to-day basis, and that strikes to the heart of what privilege is: it's an advantage that the universe just handed you. You didn't ask for it, you didn't earn it, but it's there nonetheless, making the world around you just seem to fit you better. If you have privileges, you often don't notice them unless you look for them or someone points them out.
What are my other privileges with regard to my writing career? Being born into a family that loved books was a big one. If someone doesn't teach and encourage you to read, if nobody hands you that first amazing book and says "This is cool; I think you will like this" the spark doesn't get lit. You go do something else with your life instead. Writing is a learning-intensive occupation; there are lots of individual skills you have to master and internalize to write a publishable novel.
I'm a product of public schools, but my parents bought a house in the best district in town. And that took a middle-class income that lots of families didn't enjoy. It also involved my parents caring that I got a good education; that's another advantage I had that some of my friends whose parents thought of school as free babysitting really didn't.
Other things? As a teenager, I said I wanted to write, and my folks didn't just laugh at me and tell me to get my head out of the clouds. They got me a typewriter, and later, bought me a computer. More money! Not lots, but more than some folks had. Also? That whole education thing: my parents didn't make me get a job when I was a teenager because they wanted me to focus on my grades and get into college. And it worked; thanks to them not making me work on anything but school, I had a very high GPA and got a full-ride scholarship at a small state university. And looking at the student loan debt many people are laboring to pay off now, that feels like a big damn deal. (Did I have any prospects for getting into a school like Yale or MIT? There was never any suggestion I might get into a school like that, and so I didn't try. That's arguably a point of non-privilege.)
But the other part of that is, I never had to work in fast food or retail on the weekends in high school. I got to work on getting my first 1,000,000 words of bad prose out of my system instead. And that's a privilege.
Did I grow up in a small, isolated city? Yes; I had a lot of learning to do once I got out of there. Did I grow up in a sexist culture in which my needs and safety were regularly treated as less important than men's desires? Yep. Was a close family member emotionally and sometimes physically abusive? Why, yes. Did I nearly get raped when I was 12, and suffer from untreated anxiety and depression for years and years afterward? Yep yep.
But those disadvantages don't erase the other advantages I got. Privileges aren't "bad". Everybody wants them! They don't remove the need for hard work, usually ... but they do often make your hard work pay off more quickly and with much bigger results.
So when someone asks you to check your privilege ... he or she isn't calling you a bad person*. He or she is asking you to reconsider your statements and beliefs in light of advantages (your gender, your race, your socio-economic class, etc.) that you have that you might not be taking into account.
* Well, not unless he or she phrases it like "Check your privilege, you morally bankrupt dingleberry!" Then it's a clear case of insult. But you should still probably check it just to be sure.