In amplitude modulation, the modulation index m, is kept less than or equal to 1 because

The modulation index is given by:

Where A_m is the message amplitude and carrier amplitude. If m > 1, them the amplitude of the message signal is greater than that of the carrier signal causing distortion of the message. Instead of the carrier wave with larger frequency enveloping the message signal with less frequency, we get both the frequencies interfering resulting into distortion of the message.