Just a little surprised you took PUP to 75 before and don't quite understand maneuvers =\ They do anything from trigger a JA attachment (light maneuver for Flashbulb), promote use of particular weapon skills (dark maneuver on Valoredge frame to force Cannibal Blade), or just bolster the effect of certain passive attachments (thunder maneuvers to increase the base double attack from the Coiler).
What's much more complicated (and useful) to understand is overload. Simply speaking, using a single elemental maneuver too often can cause the master to overload which prevents any maneuvers from being used for a varying duration. This does not make the automaton useless; however, it certainly affects its behavior that you should be properly influencing with maneuvers. Helpful details about overload can be found here : http://wiki.ffxiclopedia.org/wiki/Overload
I love PUP. From the appearance to the play style. I use mine mostly for soloing and lowman scenarios. Especially since they patched the A.I. of the mage frame, PUP is a par monk with a versatile pocket white mage. It's not keen at staggering in abyssea, so solo play is perfectly efficient. But you can sub THF and with a tarutaru sash and Dread, you can have TH4 (I enjoy farming this way). Most PUPs will tell you, it's pretty much about the fun, though.