I’m confused about the difference between BMX hubs (rear wheel axle). I have heard about freecoasters and cassette hubs, and I don’t have a clue what they are. Which one would I have on my BMX? It’s just a standard BMX that my mom bought me for christmas. All help greatly appreciated.

Freecoasters are designed specifficaly to allow you to roll backwards on your bike, with the cranks staying in the same position.(ie: the cranks won’t roll backwards). You can tell if you have one by walking your bike backwards and seeing what the cranks do.
Freecoasters are used mainly for Flatland BMX, since we do a lot of backward rolling tricks, and need the cranks to not move.
Cassette hubs are standard on 99% of BMX Bikes, so if your is from the store, I’d bet a million bucks it has a cassette hub. They are usually stronger, and require less maintanance than Freecoasters. They also have that distinct ‘clicking’ sound when you are rolling.
The good thing about Freecoasters are, that you don’t have to pedal backwards when you are doing a fakie, but otherwise, in Street and Park, and especially Dirt, you won’t need a freecoaster, cassette will do just fine.