These days, 'MP3 players' are an endangered species. The one exception is the iPod Touch. This has survived for a couple of reasons, with music probably being one of the lesser ones.
The four-inch Touch is essentially an iPhone without the cellular access. In other words, it has a full browser, app store, 5-megapixel camera and almost everything else an iPhone has. Oh, and it plays music, too.
Because it doesn't need the cellular stuff, it's quite a bit lighter than the iPhone. It's also less than half the price (of an iPhone 5).
All of this has combined to make the Touch an entry-level tablet for kids.
Technically, it's still a fine music player. Although it has just 16GB of storage (which is about enough for 4,000 songs if you don't store any photos or games), it can also use services such as Spotify via its apps.