To understand how electricity has power, it is helpful to first begin by thinking about how water has power.

Imagine that you have two buckets of water connected by a hose. If you raise one bucket above your head and leave the other bucket on the floor, then water will flow from the higher bucket to the lower one (this is a concept called potential energy). With this flow of water, you could do all sorts of useful things like turning a turbine. Roughly, this is how water "has power".

Electricity has power in the same way. Batteries (or wall outlets) have two terminals one labeled + and another -. You can think about the + terminal as the water bucket raised above your head, and the - terminal as the bucket on the ground. When you connect these two terminals using a wire, electrons (like water) flow from the + to the - terminals. As with the water, these flowing electrons can be used for useful tasks, such as powering electronic devices like computers.

Electricity only has power if there is a difference in electrons between the + and - terminals. This is why batteries eventually run out. After all of the electrons have flown from the + to the -, there is no longer any flow, and there is no more power in the battery.

We can understand those in the picture of energy. Energy can take different forms, such as kinetic energy, potential energy, etc. Energy is conserved and can be transform from one to another.

Back to your question, electricity has power because the existence of electric fields can govern the motions of electrons and such energy can be transformed and then it appears having the power to do other things. .

I can give you an example:
billiard. I use the billiard pole and kick the white ball, then it moves and hits the black 8. Because of the collision, the white ball stops its motion and the black 8 starts moving. Here the moving white ball behaves like the electricity. It is moving and has the kinetic energy. After the collision, the kinetic energy is transferred to another ball and it is why it stopped its motion and then the other ball started moving.

Just keep in mind, you have to kick the white ball to make it move, so is electricity (you have to generate electricity first).

We can generate electricity in different ways, converting energies of other forms into electricity. Then we use it to do different things and transform the energy into other forms. That is why the electricity had power.

Anything that contains energy has power , and the separation of electric charges consumes energy, which means that the release of those electric charges so that they can come together again (i.e. electricity) produces energy. It's the same reason why if you pick up a ball and drop it, the ball will strike the ground harder the higher you hold it when you let go. Gravity, too, has power, and for the same reason as electricity.

I hope I answered your question.

It is useful to compare an electric current flowing in a wire to water flowing in a river . The water upstream has a higher potential energy than the water downstream. I can convert the potential energy into work by allowing the water to flow through a waterwheel or mill.

Work is the term that physicists use for the type of energy that can be used to move something. Similar to a waterwheel, I can convert electrical potential energy into work by running the electric current through a motor or electrical appliance.

Power is actually a measure of the amount of work done per unit of time, so it is measuring the rate of work being performed. Doing a lot of work really fast requires a lot of power. Doing the same amount of work but slower requires less power. Think again of water flowing in the river. Water traveling in a large but slow-moving river could only turn the waterwheel slowly (low power). However, water traveling in a fast-moving stream could turn the wheel muster faster (lots of power). Similarly, electrical power measures the rate that the electric current is being used to perform some task.