Specific explanation? "rozumieć": - to understand "pojmować" - connected with a concept/idea/notion: so: I know how to solve it..., I catch it, I see, I now what you mean..., etc
"Rozumiem o czym mówisz": I understand what you're talking about. "Pojmuję to ćwiczenie" used rarely today: "I understand an idea of how this exercise is made and what to do with it.
rozumiem that is ja rozumiem - I understand. The Polish language is the so-called pro-drop language, meaning that you can drop a pronoun standing before a verb. It is possible because the function of pronouns is doubled by verb endings.
Pojmować suggests to me greater (and perhaps more prolonged) intellectual effort. It's equivalent to English 'hands-on, holding' metaphors of understanding like 'grasp' (something you do with a problem once you have been 'grappling' with it). The colloquial English to get your head around s/thing is quite close here in meaning, if not register.
A couple of quick examples snaffled off google:
1) Jak chrześcijanin powinien pojmować rolę rodzin -> 'How should a Christian conceive the role of the family' 2) Nie pojmować otaczajacego nas świata -> 'Not to understand the world around us'
... both rather tougher tasks than, say rozumiem o co Ci chodzi.
w moim pojęciu is an expression used when someone tries to pretend he speaks in intelligent way. It is a more sophisticated way of saying "uważan, że" ;DDD