Yes, any bit of luck you have that makes your life better is a privilege, because it is something that makes your life better than someone who didn't have that luck. They didn't do anything wrong to deserve not having the luck, it was just chance.

This doesn't make the concept irrelevant. It is important to accept and understand that a lot of your success in life is due to things outside of your control. You don't have to apologize for it, but you also shouldn't think you are better than people who weren't lucky.

Understanding this is important, because if you think that your success is entirely based on choices you made, you might feel like people who aren't successful are that way entirely based on their choices, too. Realizing that luck plays a big role is the first step towards understanding that those of us who have been lucky should help those of us who haven't been as lucky, because they don't deserve to be miserable just because they had bad luck.