What exactly is the energy source of tides? Tides happen due to the gravitational interactions between the Earth and the Moon. We can say that the tides are pulled by the Moon's gravitational field and so it keeps on changing as it moves out of the Moon's range. 
Now the question is: where does the Moon get the energy to be able to make the tides (pull water on Earth towards it). We all know that according to the law of conservation, energy cannot be neither created nor destroyed, so where does Moon's energy come from?
On Earth, an object (a ball) is provided with its energy/gravitational potential energy, from the energy we have from the food we have eaten, when we lift it. The source of its energy trails back to the Sun. Now can anyone please explain me where the energy source for moon is?
 A: The Moon is orbiting the Earth so it has kinetic energy as a consequence of its motion. The Earth is also rotating on its axis, so it has kinetic energy as a consequence of its motion. It is the kinetic energy of the Earth and the Moon which is ultimately the source of tidal energy. That KE is continually being reduced as a consequence of the tidal friction, but the loss is relatively small-I seem to recall reading that it will be around a billion years before the Moon ends up slowing to settle into a stationary orbit. At that point there will be a permanent high tide at the point on the Earth closest to the Moon.
A: The side of the Earth closer to the Moon is gravitationally attracted to the moon more than the center of the Earth as gravity gets weaker with distance, by the inverse square law. This causes a bulge. The side farther from the moon has less gravitational pull from the Moon, so it bulges away from the moon. As the Earth spins these bulges move around the Earth, pulled by the Moon's gravity. It is the Earth's spin that provides the energy to move the tides, so the Earth's rotation is slowed by a very small amount each day, making the days minutely longer. Earth's rotation could eventually slow enough for it to become tidally locked to the Moon, but it is expected that the Sun will become a red giant before then.
A: The other answers have (rightly) explained that the interaction between the orbit of the Moon and the rotation of the Earth are the cause of lunar tides (there are also solar tides, but let's put them to one side for the moment).
However, reading your question again, I think you already know this. So your question is really based on Personal Incredulity - you don't see how enormous effects like tides can be powered for millions of years by the Moon's orbit and the Earth's rotation. In that case, you need to do some sums.
To get a rough order-of-magnitude comparison, get the speed of the Moon (29 days at radius of 380,000 km) and its mass and so get its kinetic energy. For the tides, imagine an area water of, say, 5% the Earth's surface raised up through 1m. That gives you the potential energy in a high tide. Compare the two numbers. What ratio do you get?

 I get something like $10^{11}$ - so the kinetic energy is enormously larger.

