ok lets try this been a while since played and not played any of the Episodes but here goes
In original HL2 you figure out that earth is being run by an alien combine (i.e. multi species government of indeterminate structure) with the former administrator of Black Mesa (the location of HL1) acting as the Administrator of Earth, i say admin because its obvious the combine could undemocratically remove him at any time it suits them. the electric aliens are persecuted by the combine to the possible point of xenocide, the combine came to rule earth after a war of 7 days. the old Black Mesa team lead a resistance movement with limited success against the combine. and finally i would suggest that the "GMan" of HL1 works for a movement opposing the combine either for the sake of opposing the combine for some reason or has ulterior motives to see Earth free of combine control. with the death of the administrator the combines control is weakened and GMan intervenes but for some reason dint pull you out.
anyone who played the episodes elaborate on this?
Pretty much correct, but a few details are off.
Explanations and elaborations below.
The death of the Nihilanth (giant boss alien at the end of HL1), escalated the portal storms to a global scale, rather than just centered on Black Mesa. This is why so much Xen wildlife is on Earth in Half-Life 2. All this interdimensional activity got Earth noticed by the Combine, and they saw a juicy new conquest.
The war lasted 7 hours, not days.
Breen, that is, Black Mesa's admin, was appointed as Earth's administrator as a reward for collaborating: it was he who formally surrendered Earth to the Combine, rather than allow the human race to get wiped out completely.
The Vortigaunts were slaves of the alien race that invaded Black Mesa, and thus don't hold any particular ill will towards humanity... with the death of the Nihilanth they were freed from their slavery. Naturally, the Combine tried to oppress them as well, hence why they sided with the human resistance.
As for the G-Man, exactly what his goal is is unclear. He seems, for the most part, to be working against the Combine, but not necessarily for the benefit of Earth (there's some evidence that he might have caused the Black Mesa incident in the first place). And in fact he did pull Freeman out after the explosion on top of the Citadel: the Vortigaunts used some pooled uber-mind powers to repel him and bring Freeman back. (This is, incidentally, the only time in the series that something has apparently happened against the G-Man's will.)
It wasn't so much Breen's death as the destruction of the Citadel that weakened the Combine's hold...
...but that and the rest of the story is told in the Episodes, so I'll stop there.
Except for a couple of sentences at the end, all of this is available in Half-Life 2, but you have to look for it. Largely listening to little comments made by the characters, and those newspaper clippings in Black Mesa East. The "All-Knowing Vortigaunt" gives some more info, but he's well-hidden.
