Gravity is a concept without true explanation. It is a description of what happens, but there is no firm proof of a cause or a why. We know that two masses are attracted to each other in proportion to each mass and related to the distance. So we gave that phenomena a name: gravity.
We know lots more about gravity, like how quickly one mass can notice that another mass moved. The forces move at the speed of light. We also can predict that anti-gravity would use energy, because otherwise we could create a perpetual motion machine by turning on and off a free anti-gravity.
So in simple terms, a rocket or helicopter are antigravity machines. The machines are propelled one way by throwing mass the other way. The rocket brings the mass with it and throws that, while the helicopter just grabs the air around it and flings it down.
Imagine you are in a canoe on a lake. When you push on the water with the paddle, you propel the boat forward. This is the same method the helicopter uses. If you had several buckets of water in the canoe, and threw them one by one out the back, then you would coast forward. This is the basic mechanism of the rocket.
For fun, I have collected some classic and funny videos showing antigravity in action. The how to videos are also included.