Like a JFET transistor, a MOSFET consists of three layers of P and N silicon, where one of the layers form a channel between the Source and the Drain. However, a MOSFET looks a bit different. Let's take a look at the inside of an N-channel enhancement MOSFET:

The two N layers are connected to Source and the Drain. The Gate is connected to a layer of metal. Between that metal layer and the P layer, there a very thin film of insulating material (SiO₂). The P layer is connected to the Bulk terminal. In nearly all cases, the Bulk is internally connected to the Source. The metal layer and the P layer make a capacitor. Let's apply some voltages across the transistor and see what happens.

If V_GS=0V, the D-S channel is closed, because there is always a reverse-biased PN junction.

If V_GS>0V the metal layer becomes positively charged. The metal layer will now attract the electrons in the P layer. Thus, a layer of electrons is formed.

These electrons make the P layer close to the gate look like N silicon. And now the're a channel of free electrons between the Source and the Drain making current flow possible.

If V_DS is small, the channel acts like a resistor, which resistance is controlled by V_GS. However, if V_DS increases, the 'gate-bulk capacitor' will decrease at the Drain side. This will narrow down the channel. At a certain threshold voltage, the channel will be pinched off, and I_D will remain constant.

Depletion MOSFETs look very much like enhancement MOSFETs:

Please note the thin layer of N silicon near the gate. This means that even if V_GS=0V, there already is a conductive path between the Drain and Source. Increasing V_GS makes the path wider. Making V_GS<0V narrows the channel down.