What happen between Half-life and Half-life 2 ?

I read somewhere that HL2 takes place 20 years after HL1, and I know there was some war going on Between the combine and the earth, but that's basically al I know.
what's the purpose of City 17? Why is Freeman so important? what's the connection between all of this and the events of HL1?
Sorry for my bad english.

Between Half-Life and Half-Life 2, the main character, Gordon Freeman, was believed to be dead, but later turned out to still be alive [1, 3]. During this time, Earth was being occupied by a mysterious alien race known as the Combine [3]. Gordon Freeman was important because he was a threat to the Combine (and their boss, the G-Man) [4]. Freeman was eventually "redeemed" and allowed to live again, but he had to work for the G-Man (enabling him to continue his work) [2, 4]. During this time, Freeman's girlfriend, Alyx Vance, secretly mounted a resistance to the occupation of Earth by the Combine (with the assistance of her father, Eli Vance) [3]. Eventually, the Combine were defeated and Earth was saved [3].
The only significant events that take place between Half-Life and Half-Life 2 are the invasion of Earth by the Combine and the ensuing war. [3, 4]  Gordon Freeman is woken from stasis and joins the resistance against the Combine. [1, 4]  The Combine are the main antagonistic force of the Half-Life series, and they currently control Earth. [3, 4]  It is also unknown whether Chell survived following her escape from Aperture Laboratories. [7]