Modulation is method to impose signal on carrier frequency. There are many methods to do this. Amplitude modulation is one of those methods. In this method signal and carrier frequency are mixed in such a way that amplitude of carrier frequency changes according to signal. This is very old method. In this method there is a lot of noise. in simple it is also called AM modulation. Its range according to other methods is long for transmission but there is lot of noise which is added automatically. It circuit and working is very simple. it is shown in figure.
Keep in mind when amplitude modulation is done there are two signal bands. One upper side band and other lower side band. One of these bands are transmitted some time both of the bands are transmitted and in receiver one band is suppressed and other is demodulated to get signal. In old system of radio there was AM modulation used. Now it is also used but very rarely.