Consider an NMOS transistor. The polysilicon, silicon dioxide(insulator) and the P substrate layers acts as a capacitor. When a positive gate voltage is applied, the electrons (minority carriers) in the P-substrate are attracted and starts accumulating in the channel. It is to be noted that the width of accumulated electron channel will be higher at the source edge and gradually decreases towards the drain.
When the gate voltage crosses the threshold voltage ( Vth~ 0.7V) an electron channel is formed between source and drain and current can now start flowing.
MOSFETs have a forth terminal taken out from the P-substrate(body). Consider the case when the the body is at a lower voltage than the source. Then it is like a reverse bias applied between the P-N junction and the width of the depletion region increases. Now it becomes more difficult to bring some electrons in the channel. It takes a higher threshold voltage(~0.8V) to form a conducting channel.
This undesirable effect of change in threshold voltage due to a bulk-source voltage difference is called the body effect.
In order to avoid the body effect, the body and source terminals are usually shorted internally.