Non modular PSU have ALL the cables attached.
Modular PSU's have mostly removable cables (PCI-E connectors, SATA and Molex)
Fully modular PSU have ALL removable cables.

Modular PSU's you can choose which cables to attach. Whereas a non-modular psu, all the cables are permanently attached.
Modular PSU's are usually for people that care about how the inside of their case looks, or for people building inside small cases.

 
	