Basically any change in energy is doing work. If you lift something 2 m up and you want to know the change in energy then you would probably think first of gravitational potential, but the work formula works as well, only it's probably simpler to go the first way. You aren't changing the gravitational potential, you are doing work on the thing. Power is the rate at which you do work or the rate at which you change the energy.
The formula P = Fv is just using P = W/t = (Fx)/t = Fv
Eg.
A 1000 kg tree is dropped by a plane that's standing still in the air about 10 m above ground. Later on, the tree is 5 m above ground. What is the change in energy.
If you use mgh change in energy = 1000 x 10 (10-5) = 1000 x 10 x 5 = 50 kJ
If you use the work formula, change in energy = Fx = 10000 x 5 = 50 kJ (remember energy is a scalar quantity)
Because a = 10 m/s/s down
And as F = ma
F = 10000 N down
So same result
hope that helped