Fully Modular Power Supplies (or PSU's) Have NO cables plugged in permanently. They come with the required cables in the box, which means if there are any cables that you don't need, you don't have to have the wire taking up extra space and looking clumsy in your system.
Non-Modular PSU's have ALL of the cables permanently attached to the PSU. None can be added or removed, for all-intensive purposes. There is no real disadvantage other than the aforesaid issue of having cables that are not in use.
Semi-Modular PSU's are just how they sound, some of the cables are fixed, some cables can be plugged in or out. The cables that are fixed are usually the obvious ones:
ATX (Motherboard) Connector
EPS (CPU) Connector
Occasionally a PCI-E...