Aquaplaning occurs when the tire of your car can no longer displace enough water and it rises, therefor losing contact (and all grip) with the road.
It happens to varying degrees, and it’s not always as noticeable, but it is usually caused by worn tires with low tread depth.
The video posted here, courtesy of TyreSafe, goes into detail regarding the phenomenon, using animations and a real life test to illustrate what it is and how it manifests. They use two Lexus IS models fitted with the same make and model of tire, but one has tires that are considerably more worn than the other – they are still within the legal UK limit, though.
Watching the video, you don’t need to be an expert to see the difference between the two instances. Were you to be required to swerve to avoid a sudden obstacle in the road, in conditions simulated for the purpose of the test, you would probably not be able to in the car with worn rubber.