The amount of acceleration an object near the surface of the earth exhibits due to Earth's gravitational field, earth gravity is equal to 9.8 meters/second2. Also known as a 'G', as in "the pilot pulled 3 Gs". In this case, it is used as a unit.
It is often best to consider gravitational accelerations as a force per mass, since we perceive gravity only indirectly, as the force which counteracts it (the floor pressing up on your feet, the chair pressing up on your bum, whatever). This acknowledges that we are not actually accelerating at 9.8 m/s2. Phrased in this manner, earth gravity is 9.8 Newtons/Kilogram.
Evilkalla: if you're talking about spacegoing objects, well of COURSE g is going to be different. That's hardly on the surface anymore, is it? But even more deeply than that you are correct - that the earth's surface has all the same potential merely means that the direction of the gradient of the potential at any point will be straight down, and not that its strength will be the same everywhere. Still, the value is, to two significant figures, 9.8 meters per second.