For Explorer's Guild, the movement points come from an ancillary that the guild has a chance each turn to grant to any general there (the ancillary grants 15% extra movement points). I'm not sure if that's the guild's only intended function or not, but the anicillary does work at the moment.
I've never had it Foz, but accordding to those that have, the description says it gives a movment bounus to EVRYONE in your empire. I can't see anything that does that, just the one ancillary you mentioned.