An important thing to note to start out is that these ‘episodes’ are being developed by Valve itself, which is a relatively rare thing in the gaming industry as most expansions are outsourced to another (often smaller and unproven) gaming company. But Valve felt it only really mastered their Source engine after finishing HL2 and that the expansions were a perfect way to showcase their full ability. And I can already tell you: they weren't lying about that.
Unsurprisingly, Episode One picks up where HL2 ended. But as you may or may not remember, the HL2 apotheosis wasn’t exactly a gift for an expansion scriptwriter. I feel that, considering the circumstances, the creative boys and girls at Valve did a good job working around this by having Vortigaunts intercept Gordon Freeman (aka you) and Alyx seconds before they would have been blasted to chili meat by the explosion. Anyway, so the Citadel’s reactor core is about to go boom and you and Alyx wake up smack in the middle of City 17, right next to the Citadel. You’d think the Vortigaunts would have the decency to teleport you outside the freaking city, but that’s just me being an ass about plotholes. From that moment on you and Alyx are involved in a race against time to get away from the Citadel and City 17 – which is pretty much the basic plotline of Episode One.