A carbonyl is the group C=O in a molecule. It is a carbon and an oxygen atom with a double bond between them. Carbon has another two bonds, which can in general be with any other group. For example, a carbonyl is the C=O bit of a ketone, aldehyde or ester.
Because oxygen is more electronegative than carbon, the electrons in the bond are more towards it. This means that in acid, a proton will go on the oxygen atom. Both the carbon and the oxygen in the group are sp2 hybridized.
The carbonyl is a very important functional group, because chemists can do many reactions with it. It is easy to do nucleophilic additions to it, which makes the molecule bigger. It is also easy to do redox reactions, for example forming an alcohol. The alcohol then is also a very useful group.
Carbonyls are found in many natural substances and also in drugs and medicines. It is easy to check if a carbonyl is in a molecule. It gives a very strong signal in infrared spectroscopy. In carbon NMR spectroscopy, the signal is usually at very high frequency, away from many other peaks.