Thrust is a force, a "push" or a "pull". If you push or pull something and it moves you are doing work. The rate at which you are doing work, ie how long it takes you to push or pull an object to it's new position, is power.
If you could stand an aeroplane on it's tail so it is pointing vertically upwards and generate enough thrust to overcome the weight (and any drag you encounter when moving) you will achieve the best angle of climb (Vx = 90 degrees). But the rate of climb might be very slow, ie only rising one foot every minute. To achieve the best rate of climb you need maximum power ie the best rate of doing work. It also helps if you are at a speed where the power required to move the aeroplane is at a minimum. So Vy, the best rate of climb, will be achieved when you are developing maximum power from the engine and flying at a speed (Vy) that requires the least force to move the aeroplane a set distance in a given time (minimum power). This will get you to altitude quickest.