Vortec is GM's name for their engines that use Port Fuel Injection. Before Vortec was introduced in 1996, GM Trucks used Throttle Body Injection or TBI for fuel delivery. It was basically taking the idea of a Carburetor and adding fuel injectors at the top where the air mixed, so that it was more controllable. This helped to prevent things like vapor lock. However, in 1996 the injectors were moved from the air intake area to directly in the cylinder, GM called it Vortec. There are two versions of Vortec, Sequential Port Fuel Injection and Multi-Port Fuel Injection. The latter is what is used in todays applications. Vortec and other fuel injected engines allow for total computer control of fuel mixture and therefore increase power and theoretically efficiency of an engine. Though from my personal experience I've found that earlier Vortecs engines 1996-1998 were good for power, but slightly worse for mileage compared with TBI.
You only see Vortec engines in GM trucks, they still based on the Chevy Small Block Overhead Valve or Pushrod engine and are known for their durability.
Other manufacturers also name their engines for instance Ford Pickups are typically powered by either a Triton V-8 or a Power Stroke V-8. And Chevy also calls their Diesel engines Duramax.
So there you have it, Vortec is just GM's name for either Sequential Port Fuel Injection or Multi-Port Fuel Injection. The idea with the name Vortec is that GM's system creates a mini twister that supposedly mixes the gas and air better, now I'm not sure if it actually does this, but it sure does sound good.