Mosfet n+ region significance
Historically, the contacts to the drain and source regions of a transistor used aluminium. This aluminium would be contacting the semiconductor. In the case of an Al-p or Al-p+ contact, we would have a normal, ohmic contact behavior. This is what we desire - if we increase the voltage, the current increases too in a linear manner.

Things are different when we build an Al-n contact. When we do this, we have actually made a Schottky barrier! The contact will behave as a Schottky diode, only conducting current in one direction. To counteract this behaviour, we need to more strongly dope the immediate contact area. While this will not make the contact ohmic, it makes it conduct in both directions in a somewhat linear manner.