Okay kiddo, so imagine there are two groups of people: young people who like new and exciting things, and older people who prefer things that have been around for a while.
Well, a young fogey is someone who is young but acts like they are an older person. They tend to like things that have been around for a long time, like old-fashioned music or clothes, and they might not be interested in new technology or trends.
It's kind of like when you pretend to be a grown-up and wear your mom or dad's clothes or listen to music they liked when they were young. But young fogeys do it because they actually prefer those old-fashioned things over new and trendy ones.
Does that make sense, kiddo?