There is speculation - but here is the long and short of it:
HL1, gman provides the sample the makes the cascade. This alerts the giant floating last boss of HL1 aware of Earth. So he teleports minions into black mesa - war breaks out. Ultimately Barney escapes, Shepard is locked away by gman. Gordon fights and helps the science guys stop the portal storm that was created from the cascade (the whole rocket mission), then they find that some large thing (last boss) is teleporting vorts in still - so you go after it and kill it. Gman takes you away and nukes black mesa. If you pay attention you'll see an image of those flying mind eating things from episode 2 in half-life - blueshift.
The story is that last boss in hl1 has enslaved the vorts to be an army for [we assume] the combine. You freed the vorts (you'll notice they are missing some "armour" clothes thing that enslaved them). Now that gordon is missing, the combine (knowing where earth is) open another portal storm (bigger than HL1) and invade, the 7 hour war happens, we epic fail and Breen (Administator from Black Mesa) hands over earth. Humans are repressed from making babies (reason there are no children) - science dudes from HL1 start to try and fight back, gordon arrives and single handly kicks butt in HL2!