In performance mode you can assign up to 3 MFX (providing certain effects are used, see P75 of the manual), so if you wanted an overdrive for a guitar sound, you would select the overdrive effect (effect 2) for one of the MFX, set the part's output to that MFX, and bingo.
You can send other parts to that MFX if you wish, if you like that sort of thing.
The output of the MFX can also be sent to the 'global' chorus, and reverb programs for the performance.
In patch mode, you would only be able to select a single MFX.
The 90 MFX algorithms listed on P75 show what's on offer, featuring guitar type effects (distortion, overdrive), some keyboard type effects (rotary), a selection of studio type effects (delays, pitch shifters, reverbs), well pretty much anything you would want from a multi effect processor.
The pages that follow in the manual explain the parameters that make up the MFX effect, all of which can be altered, and some can be controlled via MIDI too (any parameter that has a # in it).
I understand it might be a bit daunting, it's quite a powerful multi effect engine in there (probably a BOSS chip set).
Way back when the JV series started, you had chorus, and reverb, this survives as the global chorus, and reverb.
Then came the JV-1080, this added a MFX to the mix, and yes it was a single MFX, and many of the algorithms are what's in your 5050.
The JV-2080 brought us up to 3 MFX's.
I think the latest Jupiter 80 4 MFX's for upper, and lower parts (8 in total) with 76 algorithms, with a reverb unit to boot.. Oh and a separate processor for the solo/percussion section with a reverb too. And you thought the 5050 was scary...