Modulation just means modifying one signal with another.
In the most fundamental kind of modulation, amplitude modulation (AM), the amplitude of a high frequency sinusoidal 'carrier' wave is made to follow the value of a much lower frequency signal. AM has been around probably longer than any of the others, but since it wastes a lot of power, other modulation techniques have evolved. Variations on AM include suppressed carrier AM and 'sideband', which are less wasteful of power.
Frequency modulation (FM) can be thought of as making the instantaneous frequency of a carrier wave to increase and decrease according to the value of the modulating signal. Phase modulation (PM) similarly adjusts the phase of the carrier. These generally require a bit more bandwidth, but tend to be more immune to noise.
There are plenty of other modulation techniques, more sophisticated than AM, FM and PM, which do a better job of getting more information across in the same bandwidth.