The Borealis has a teleportation device on it that is able to travel both time and space.
Gordan, Alyx, and Dr. Mossman are all on it as they activate it, and realize the potential this device has as they inadvertently start warping around on the ship.
Alyx, wanting to follow her fathers final wishes, debates destroying the ship with Dr. Mossman, who sees this ship as the only chance to actually defeat the combine.
Alyx kills Mossman, mainly because she never actually trusted her and always resented her for being a double agent. Alyx locks in on what she thinks is the Combines base of operations for Earth, and basically makes a mini-citadel nuke that is traveling towards the Combines base.
In the fleeting seconds, the G-Man interrupts these events and takes Alyx away. Gordan witnesses that the "base", is actually a Dyson sphere, which is a megastructure that completely surrounds a star to harness all of it's potential energy, something only the most advance civilizations are able to create.
This basically means that Alyx was an unknowing sleeper agent for the G-Man, and her plan and goal are pointless, and the ship won't actually do anything other than be destroyed, Mossman was right.
In the final seconds, the Vortigaunt intercept Freeman, similar to what they did in Episode 2, and save him, bringing him to an undisclosed location on Earth at an undisclosed future date.
TL

R. The Combine quite possibly are the most powerful civilization in all of time and space in all realities , The G-Man's plans are to destroy the Borealis and it's technology for unknown reasons, it's unknown if humanity and the resistance was successful in it's uprising on Earth.