ELI5

Someone else will probably explain this in a much better way, but I'll give it a go. I'll explain DC, AC is a bit more complex.

Current is the flow of charge. Atoms are made up of a nucleus, surrounded by electrons. The electrons are loosely held, meaning they can travel around to other atoms.

In simple terms, batteries have an accumulation of atoms with extra electrons which are lost more easily, meaning the electrons want to move away. This is known as electric potential. Since there is a lack of electrons (aka positive charge) in the opposite terminal of the battery, the electrons move from the negative to the positive terminal, or we say the positive charge moves from the positive to the negative terminal, through the circuit.

Metals are known to let charge flow within them, so they are used as conducting wires in circuits. When electrons flow through the circuit, the energy with which they flow can be harnessed. Example, if we add a resistance to their path which glows, you have a bulb.

Motors work in a different way. When current flows through a circuit, it has a magnetic effect on its surroundings, so it can interact with magnets. This is harnessed to make rotational motion. It helps if you watch videos, as the visual representation is infinitely better.

I am also still learning, so if anyone finds any mistakes whatsoever, please do let me know. I intentionally didn't use the falling water analogy, as that didn't help me at all when I was learning this topic.