Where are you in your educational progress, and how much science and physics have you been introduced to so far? Knowing this may help us to explain things at the right level.
One thing to make clear is that nobody, even the most advanced scientists, really knows "how" things happen. On some level, what happens in physics is like magic. How can one magnet attract another magnet, when the two magnets are far apart and not touching, and there are no strings attached? It is mysterious, and not something that can be explained in terms of anything simpler.
What happens in science is we observe what happens, and we find out how to describe what happens with rules: if I do this, then that will happen. We make note of all the rules and we use those rules to make predictions. In engineering we use the rules to help us design and create useful things.
One thing we can observe is that there is something called "energy". We can account for energy in all its forms, so that no energy is ever created or lost, it is only changed from one kind to another.
In a hydro plant, the water in the reservoir has gravitational potential energy. When this water flows down the pipes to the turbines the potential energy gets converted into the kinetic energy of motion. When the fast moving water hits the turbines, the kinetic energy of the water is transferred to the turbine, making it spin. When the spinning magnetic fields in the turbine intersect the wires in the coils, the moving magnetic fields make electricity move in the wires, converting mechanical energy to electrical energy. And so it goes on.