Neither.
Gravity is one of the fundamental forces, of which there are four. These are: (from weakest to strongest) gravitation, the weak nuclear force, electromagnetism, and the strong nuclear force. These four forces govern all interactions between matter and energy in the universe, and the space in which they influence each other is known as a "field". (gravitational field, electromagnetic field, etc.) For example, when one object collides with another, it isn't actually the objects touching each other; it is the strong nuclear force, which prevents particles from passing through other particles. (Although it is the strongest of the four, it only has noticeable effects at extremely close distances.)
If it weren't for the strong nuclear force, particles such as protons and neutrons(hadrons) would pass right through each other instead of bouncing off.
The strong nuclear force is also responsible for nuclear fusion: when two particles are forced closely enough that this force is overcome, it results in them annihilating each other and releasing energy. (Their mass is converted into energy. Matter is actually energy itself; just very concentrated.)
So gravitation, the weakest of the four, is responsible for gravity. (The difference being that gravity applies only to the attractive force of the earth, whereas gravitation is the attractive force between ALL matter.)
The reason we only observe the gravity of large objects such as the earth or sun is because gravitation is incredibly weak; so it's only noticeable when there are enough particles together for their collective gravity to have a significant effect on other nearby matter(i.e., meteors, the moon, us).
Gravitation is also responsible for the fusion reactions in stars.
When enough particles combine for their collective gravitational force to be greater than the strong nuclear force keeping them apart, the particles will be pulled into each other, becoming energy. Their gravity will remain, so the reaction will continue. Incredible amounts of energy will be constantly released until there are no more particles left to continue the reaction. This is known as a star.
This explanation is very basic; the study of the strong nuclear force and its interactions is called Quantum Chromodynamics, and it is one of the most complicated fields of study known to man.
I hope that answers your question; thank you for taking the time to read this.
P.S. - For a more detailed explanation, go to Wikipedia and look up "Fundamental Forces".
P.P.S - In the answer written by the gentleman above, gravity waves are briefly mentioned. In case you were wondering what that is, it is a brief fluctuation in a gravitational field that propagates like a wave.