Wheely - when performed on a bicycle is to ride along with the front wheel in the air, supported only by the rear wheel. This also works on motorcycles and grossly overpowered cars, see The Fast and the Furious.
I have no idea actually how to maintain a steady wheely once started, but this is how to get started. It helps to be in a low gear on a bicycle, as you need lots of torque. Basically while stopped or moving very slowly, you apply lots of torque to the rear wheel by mashing down on one pedal suddenly. It helps to lean back a bit, instead of leaning forward like usual; the idea here is to take weight off the front wheel, making it easier to come up. Don’t lean back too far, bad things happen. Nobody likes cracking their own skull open or breaking a tail bone trying to look cool. Once up, you just maintain proper torque/pedaling/balance to stay on the rear tire.
Disclaimer: I will not be held responsible if you break yo self.