what is energy density and power density

 Let's take the example of a car engine. You have fuel, you convert that chemical energy into mechanical and have an engine running. This allows your car to move, this solves our energy problem when we figure out which type of energy can we use to make our car move. Now at some point in time, you will run out of fuel. So the more important question for you is - When will you run out of fuel? You have limited fuel a.k.a. limited amount of energy, so if we know how much energy we use per second, or per minute, we will know when will we run out of our fuel. This is where power comes in. It's simply a calculation of how many units of energy you are using per unit of time. Depending on the situation, you can decide to use whatever units you like for energy and time. But essentially its energy/time. Work is also a form of energy so sometimes you get questions like - how much work can you do per second?

Essentially, the amount of power tells us the amount of fuel we are consuming that will determine the amount of fuel we need to keep providing for the engine to work and our car to keep moving.

One more thing. For example, if we have 250 horsepower engine, what that means is that particular engine has an upper limit. No matter how much fuel you supply, that's the absolute max of the performance you are going to get. Even if your tank is full, there is a limit on how fast you can accelerate and how fast you can possibly go.