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Gravity is a force pulling together all matter (which is anything you can physically touch). The more matter, the more gravity, so things that have a lot of matter such as planets and moons and stars pull more strongly.
Mass is how we measure the amount of matter in something. The more massive something is, the more of a gravitational pull it exerts. As we walk on the surface of the Earth, it pulls on us, and we pull back. But since the Earth is so much more massive than we are, the pull from us is not strong enough to move the Earth, while the pull from the Earth can make us fall flat on our faces.
In addition to depending on the amount of mass, gravity also depends on how far you are from something. This is why we are stuck to the surface of the Earth instead of being pulled off into the Sun, which has many more times the gravity of the Earth.
As yet gravity and magnetism are thought to be unrelated. However Einstein believed they were related but was unable to prove this mathematically.
This is in many ways one of the big questions.
Once there were 4 known forces:- Gravity and Electromagnetism, and the weak and strong forces. The last two are seen at the atomic level only.
Then it was proved that the electromagnetic and weak forces were really different aspects of the same thing - it's thought the strong is too but nobody's proved it yet.
This leaves gravity which is in many ways totally different - Einstein showed that it can be thought of as matter warping space and time, and this description has been very sucessful but it doesn't help bring them all together in one theory.
Oh and just to make life absolutely peachy, in recent years we've discovered that on the large scale galaxies are rushing away from each other faster than they should be. The energy behind this has been termed dark energy (because we don't have the faintest clue about it - not because it listens to heavy metal music) and so there might even be a fifth force related to this.
If you're young enough, bright enough, determined enough and fancy shaking the King of Sweden's hand to pick up a Nobel, one day you might be able to answer your own question properly.
Its interesting to note that compared to magnatism, gravity is extremely weak. Put a magnet on the ground and drop a small magnet onto it. If the poles are the same then they will repel eachother. In which case the magnet dropped will jump away from that on the ground. So you have the repulsion of a magnet on the floor pushing the dropped magnet up, and the gravity from the whole of this planet pulling it down. The magnet will win.
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