What exactly happens to the Traveler at the end of Destiny 2's Campaign? *spoilers*

At the end of the Boss fight with Dominus Ghaul, he becomes a giant form of liquid gold light; he then turns to the Traveler as blue lines start to form and crack under the shield the Red Legion used to trap it, and that same shield is broken by the traveler.

Ghaul then says "You do see me..." as the traveler explodes and a wave of its blue light shoots out into the galaxy with itself as the center. This is the same blue energy that can be found on Io.

What is the traveler doing here? It's never really explained in the story, but it's visible from the tower for the rest of the game.

From the wiki

Nonetheless it was captured at the start of Destiny 2 by the Cabal Red Legion and taken from humanity, weakening Guardians severely, only to reawaken after countless millennia to smite its leader Dominus Ghaul and putting an end to the Red War.

Basically, Ghaul caused the Traveler to wake up after being put under the amount of stress that "draining the Light" caused. Ghaul mistook this for "seeing him", but it's more than likely still unaware of individuals the same way a human is unaware of individual ants.

At this point however, nothing more is known about the Traveler, other than it is now "awake", as it does nothing else after this point*.

^{* I have not played the DLC, so I don't know if this uncovers anything more about the Traveler}