There are two forces in nature that we experience every day: gravity and magnetism. You may have magnets on your refrigerator, and you know that a magnet will attract a refrigerator with a certain amount of force. The force depends on the strength of the magnet and the distance between the magnet and the metal. You also know that magnets have two poles -- north and south. Either pole will attract iron or steel equally well, north will attract south, and like poles will repel one another.
Gravity is the other common force.
Each particle of matter attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The standard formula for gravity is:
Gravitational force = (G * m1 * m2) / (d2)
where G is the gravitational constant, m1 and m2 are the masses of the two objects for which you are calculating the force, and d is the distance between the centers of gravity of the two masses
G has the value of 6.67 x 10E-8 dyne * cm2/gm2. That means that if you put two 1-gram objects 1 centimeter apart from one another, they will attract each other with
the force of 6.67 x 10E-8 dyne. A dyne is equal to about 0.001 gram weight, meaning that if you have a dyne of force available, it can lift 0.001 grams in Earth's gravitational field. So 6.67 x 10E-8 dyne is a miniscule force. When you deal with massive bodies like the Earth, however, which has a mass of 6E+24 kilograms (see this Question of the Day), it adds up to a rather powerful force. It is also interesting to think about the fact that every atom attracts every other atom in the universe in some small way!
Einstein later came along and redefined gravity, so there are now two models -- Newtonian and Einsteinian. Einsteinian gravitational theory has features that allow it to predict the motion of light around very massive objects and several other interesting phenomena. According to Encyclopedia Britannica:
The general theory of relativity addresses the problem of gravity and that of nonuniform, or accelerated, motion. In one of his famous thought-experiments, Einstein showed that it is not possible to distinguish between an inertial frame of reference in a gravitational field and an accelerated frame of reference. That is, an observer in a closed space capsule who found himself pressing down on his seat could not tell whether he and the capsule were at rest in a gravitational field, or whether he and the capsule were undergoing acceleration. From this principle of equivalence, Einstein moved to a geometric interpretation of gravitation. The presence of mass or concentrated energy causes a local curvature in the space-time continuum. This curvature is such that the inertial paths of bodies are no longer straight lines but some form of curved (orbital) path, and this acceleration is what is called gravitation.
If certain assumptions and simplifications are made, Einstein's equations handle Newtonian gravity as a subset.
The question of why atoms attract one another is still not understood. The goal is to combine gravity, electromagnetism and strong and weak nuclear forces into a single unified theory. (Check out this page on quantum gravity string theory.)