What exactly is Ford's eco-boost engine?

What makes it "eco-boost" (specs/)
What does that mean?

Its a smaller displacement motor that uses a turbo or two along with direct injection, variable cam timing and other engine tech to make the same or more power as a regular engine that is much larger. And they get much better fuel mileage.
For example the 3.5 EcoBoost V6 currently makes more power than Ford's current 5.0 V8 (in the truck not the mustang) and gets alot better fuel mileage than its V8 counterpart

It uses a turbocharger to force more air into the cylinder. In a normal turbocharged engine, this raises cylinder pressure and temperature, making the fuel prone to self-igniting from the pressure before the piston is finished with the compression stroke. This causes a knocking sound, a loss of power, and will damage the engine. The normal way to get around this is to use a higher octane fuel, which is more resistant to pre-ignition, but it is also more expensive.

Ford's Ecoboost system uses a different approach. Instead of injecting fuel in the intake manifold where it is forced into the cylinder on the intake stroke with the turbo air, Ford uses what's called direct injection. The fuel injectors squirt directly into the combustion chamber, after the intake valve is closed. This does two things. First, it introduces the fuel after most of the compression stroke is finished, eliminated the window for pre-ignition. Second, it cools the compressed air charge already in the cylinder, again reducing the engine's tendency to pre-ignite. This allows the engine to run on 87 octane fuel at boost levels that would destroy a conventionally fuel injected turbo engine.

The turbo itself provides boost at higher RPMs when the driver wants more power. When it's cranking out the full 15 pounds of boost (or whatever Ford tunes them for), then it's burning just as much fuel as a V6 or V8 making the same horsepower. The fuel savings come when the car is cruising at a steady speed, and RPMs drop. The turbo spools down to a slower speed, boost drops, and the thing burns basically the same amount of fuel as a non-turbocharged 4 cylinder.

Small displacement for economy, turbo charged for power when needed.

Reduces green houses emisions, it has a better enigine.

When driving slow, and not needing much power, only some of the cylinders of the engine will fire. When more power is demanded, all cylinders will fire.