A Stargate allows you to warp in Protoss air units.
The warships of the protoss fleet require a much stronger warp link in order to materialize than a standard gateway can provide. The immense stargate is capable of calling ships from high orbit or across immense distances to appear on a planet surface. The construction of one or more stargates at a protoss base is a sure sign that it has become a major staging point for an offensive. This excerpt from the after-action report of Flight Sergeant Aaron Keebler helps underline the rapidity with which the protoss can switch their stance.
"It was a small outpost: a nexus, assimilator, and a couple of gateways. Commander didn't want to risk marines against the cannons they had dug in on the cliffs so me and the boys got brought in for a little death from above. First raid, we got a bunch of them little worker probes and lit up the pylons powering the cannon. They tore us up pretty bad, though, so we headed back for repairs.
By the time we came back, it'd all changed. Two big stargates were there, and protoss flyers were popping out of those big hoops like bees from a hive. We got hit every which way, and I only made it home on one engine and half a wing. Couple of minutes later, protoss air hit our base hard; I'm starting to think they only let me get away so they could follow me back...."