The diode in the symbol is redundant; just emphasizing that, yes, there is in fact a diode here. It's often drawn as a zener to indicate avalanche robustness.
The structure of an N-channel MOSFET consists of two N-doped regions embedded in a P-doped substrate. Thus there is an intrinsic diode (P-N) from substrate to each terminal. Three-terminal MOSFETs always tie substrate to source. (The most common exception is probably when the substrate doesn't exist at all, as in power GaN MOSFETs: the GaN is a thin active layer on top of an insulating layer. 4-terminal MOSFETs are rare but do exist.)
The depiction has three vertical line segments in a row, indicating the drain, channel and source respectively; the arrow/triangle indicates the substrate P-N junction. The lines are broken, indicating the channel is normally in depletion i.e. current doesn't flow at Vgs = 0. Positive gate voltage enhances (hence "enhancement mode") or induces charges to the surface, making it conductive (the surface of the P-substrate becomes N-type, connecting drain and source resistively). A depletion-mode MOSFET should be drawn with a solid line segment, indicating the channel is normally conductive at Vgs = 0 (and is turned off by negative gate voltage).
As far as understanding operation, it's just a 4-terminal MOSFET with source and substrate tied together. It sounds like you already understand the 4-terminal MOSFET, so this should be adequate.