Do you know any famous people? Do you want to make sure that *everyone* knows you know famous people? If you say something like "I just went to lunch at that restaurant the other day. I was with Felipe and Leti - that's what her close friends call her. He really liked the food, but I didn't think it was very good." then you have just "dropped a name." Basically it means mentioning famous (or important) people in a way that shows that they're your friends - or at least that you know them. It is usually used with famous people, but you can also do it with people who are important in a specific context (for example, in a university, you can name drop the university president). "Name checking" is another phrase for the same type of thing.

As the member above mentioned, it's using the names of famous people in everyday conversation to show a personal connection to them and thus seem quite important yourself. In my opinion, a casual attitude towards the famous people you mention isn't required to be 'name dropping' but it certainly happens.

Example: "We just had the most fun party at our house, and lots of people came by, you know the normal: Beyonce, my friend Luke, my mom, etc." It's like casually mentioning someone famous or important and your interaction with them. You make it seem like it wasn't that big of a deal to you to interact with that person, which is supposed to make you seem cooler because you're not all that impressed.