Gravity is what makes the moon orbit the earth, and is also what causes the planets of our solar system, along with all of their moons, to orbit the sun. It is basically what holds our whole universe together. According to Isaac Newton, gravitation is a type of force. In physics, force is simply a measure of push or pull. The greater the push or the pull, the greater the force.
Gravity is an attractive force that affects everything in the universe. In other words, gravitation is the force that pulls all things towards each other. You can see gravitation acting in our solar system, for example through the Moon's circling of Earth. This is because the Earth and the Moon are pulling towards each other. Even you and the computer monitor that you are looking at are pulling towards each other, but since both you and the monitor have very small masses (meaning that you both are very light) you cannot really feel the force between you. However, you can definitely feel the Earth pulling on you; this is because the Earth is so massive.