Implications
The law of gravitation states that physical bodies attract with a force proportional to their mass. This force is what keeps the Earth orbiting around the sun, the moon around the Earth. This force is also responsible for the coalescence of dispersed matter -- the forming of matter into spherical entities such as planets.
Why We Orbit
One might theorize that because of these gravitational forces, the planets should eventually plunge into the sun. For many astral bodies, that is exactly what happened. The initial position and velocity of objects when the solar system first formed determined their fate. Objects moving toward the sun got sucked in and helped form the star. Objects on a path away were flung out of the solar system much like Apollo 13 was flung around the moon by its gravitational force. Only a small percentage of bodies were in the optimal range, with the optimal velocity, to attain sustained orbit. They won't plunge into the sun because their centrifugal (circular) force keeps them in permanent orbit.
History of Gravitation
Modern gravitational theory started with the work of Galileo in the late 16th and early 17th centuries. He found that gravity affects all objects at the same rate instead of the prior notion that heavier objects fall faster. Isaac Newton later discovered the force of gravity on the Earth's surface was about sufficient to keep the moon in orbit -- a theory he quickly applied to all astral bodies. Finally, in 1915, Albert Einstein contributed to two theories that brought gravitation to its status as an accepted law of physics.
Equivalence Principle
The equivalence principle relates to the idea that all objects speed up in the same way from gravitational forces. For example, two objects that have different masses (i.e. they would weigh different amounts on Earth) that are dropped will hit the ground at the same time, provided there is no resistance such as wind. This idea evolved into the idea that the direction of mass that moves in a gravitational field depends only on starting position and speed as opposed to what the object is made of. Therefore, planets will orbit based on their starting position and speed when the solar system was formed even though they are all made of significantly different materials and have different masses.
General Relativity
General relativity is another critical theory that complements the force of gravitation. It explains how mass can have an influence on the passage of spacetime. For example, radio signals sent toward Earth from the other side of the sun will be slowed by the sun's mass and delayed in reaching their target. Much the same way, Mercury's orbit doesn't perfectly conform to gravitational force expectations (its orbit shifts more than expected by gravitation alone) because of the impact of general relativity.