A person in just about any Halo game(more recently Halo:Reach) who is of a high rank, yet is terrible, immature, a squeaker, talks too much shit, uses detachable turrets, rushes power weapons, betrays teammates for said power weapons, or overall is just a bad player of Halo. This mostly pertains to Reach since the rank of the player is determined by the amount of overall time the player has achieved in multiplayer(credit-based ranking system.)
Most PseudoPros usually boost, either by full-party methods or by challenge boosting. In other Halo games like Halo 3 it can be detected by people who brag about armor, achievements, or anything really.
Basically, if you run into a Halo PseudoPro, please for the love of god, do not friend request them just because they are a Forerunner/50/have all achievements. Also, do not pay any attention to their unnecessary teabags/hate messages/general asshole behavior. They just want attention since their mom/transvestite dad stopped breastfeeding them.
Me: I ran into a Halo PseudoPro today, all he did was teabagand brag about his Hayabusa armor, even though the year is 2011 and everyone who has the campaign disc has it. Friend: wow someone like that must just have a tiny dick/enflamed cliteris and feels like they need attention, what an asshole.