Can somebody help me understand batteries?

Question

I'll explain what I know, then, you can tell me if I'm right or wrong.

I know that a battery consists of three main parts: the anode, the cathode, and an electrolyte. The anode is electropositive and the cathode is electronegative. The electrolyte is a nonconductor of electrons, and it keeps the anode and the cathode separate. When connected to the cathode with a wire, the anode oxidizes, and the electrons that are released flow across the wire. The flow of electrons is electricity. The electrons are combined with the atoms from the cathode. The flow continues until the materials are used up, and the battery dies.

Am I correct? I feel like I am missing something. If I'm wrong, please correct me.