Aristotle developed the first theory of motion (among other things) and got it wrong. Unfortunately it is the theory that most people use to describe how things move.
The theory stated that everything is in a state of rest until you give it a push. Seems reasonable: you are sitting down and not moving. And until your muscles give you a push you will not start moving. It was a pretty good theory and stood the test of time until the 17th Century when it was buggered up by the all new, never before published Newton's Theory of Motion.
Newton's Theory of Motion says simply that everything is stationary or keeps on going until you give it a push.
It works like this: Imagine a ball bearing rolling along a very long (infinite) table. If we ignore friction and air resistance, the ball bearing will continue to roll forever until you stop it.
Imagine an astronaut floating in space. He will continue to float along until he whacks into something. But what (I hear you cry) about me sitting in front of my computer. Well if the ground was not underneath you would fall towards the centre of the Earth - it is the ground that stops you moving. Why do you fall to the centre of the Earth? Newton solved this puzzle as well - he worked out that everything is attracted to everything else - gravity is what glues the Universe together. It is what keeps us in motion.
Newton's Theory (once it became accepted) solved many of the problems confronting scientists. And it is still pretty good for calculating things such as how to catch a balll or get a man to the moon.
Unfortunately (again) is was not very good at explaining very small and very big motions: atomic structures and the shape of the universe itself.
This is where is gets a bit complicated. To solve these probelms two new theories were introduced: Quantum Theory for atoms and Relativity for the universe.
Everything can be broken down into tiny packets or 'quanta' of energy. It's true, light is composed of photons, tiny blobs of quantum energy. We can even count them using special sensors, it is just that there are so many of them that all we see a continuous beam.
When a photon collides with an electron there is an increase in the quantum energy of the electron. This makes the electrons jump into the next quantum energy level - the size of the jump is dependant on the photon energy. Electron do not like being in this high energy or exicited state and will soon jump back to their original position and in doing so will emit a photon. This is happening all the time, it is the reason why this computer works, your heart pumps and the sun continues to shine.
This is really all you need to know about quantum theory: energy is absorbed or emitted by atoms in tiny packets which move on to the next atom and so on and so on forever.
To appreciate quantum theory, you need to suspend common sence. The quantum jump is a real jump, there is no movement from A to Z passing though all stations in between. There is nothing between A and Z in the quantum world.
The good news is that quantum effects can only be observed in atoms. The jumps are just too small to be noticed. Even so, every move you make is the result of billions of quantum jumps - the end result (for us) a seemingly smooth transition. Which is why we can use Newton's Theory of Motion in every day life (the fastest computer in the world could not calculate all the quantum changes needed to even blink your eyes).
Relativity was Einstein's great work. He worked out that because everything is attracted to everything else (gravity again) the motion of each of the bodies in the universe affects the motion of everything else.
Imagine a big metal ball plonked in the middle of a rubber sheet. The weight of the ball will stretch the rubber sheet, make a bit of a dip in the middle. If we put another ball on the sheet it will roll towards the dip. But if we whizz it around the dip it will orbit the heavy ball. Now obviously the Universe is not made of rubber but the same thing happens in space. Heavy things like stars 'distort' space attracting plants towards them and even bend light waves.
Einstein worked out that everything in the universe can be represented as an energy source. If you know the energy value of everything you can work out the distortion and therefore how it everything will move.
This is General Relativity and can be summaried as: matter tells space how to curve, space tells matter how to move
Special Relativity on the other hand is more to do with how we observe things. If you follow a cyclist you will see the pedals going up and down. Somebody else standing on the pavement will see the pedals going round and round. It is the position of the observer that determines what is observed.
The next stage is consider the speed of the motion. Without the mathematics, special Relativity can be summaried as: moving clocks slow down and moving bodies get smaller.
The good thing is, relativity has little effect on us here on Earth, we do not have enough energy or move fast enough. So Newton's Theory is good enough for most calculations.