I saw the sentence “Check out my social media feeds.” What’s that mean?
"Check out" in this context means "take a look at" or "consider".
"Medium" in this context means "a way of sharing information". Newspapers, magazines, radio, and television are all kinds of media.
Some examples of "social media" include blogs that have comment sections, Facebook, Twitter, and Stack Exchange.
"Feed" in this context means "something that provides updates whenever new content is available". A physical example is an ammunition belt that feeds cartridges into a gun. In the "social media" context, a "feed" is a piece of software that provides notifications when new items have been posted to a social medium.
The person who is holding the phone is checking out someone's Facebook feed:
Facebook is a social media network. Of course, you can say, for example, "Twitter feed." If you want someone to check out your feed or feeds, you want them to see it or them for the first time. You check out a website in the same way. So, "check out" means visiting a page for the first time, but "check" means you've done it before.