I saw this story on the BBC website, read it and felt like someone had plunged my brain into fog. I can only assume that the journalist either doesn't understand the subject very clearly himself, or was in a hurry. It isn't often I feel that understanding has been sucked out of me and replaced with confusion.
So, I went searching for a better explanation, and found it on the ESA site. There is a PDF to download which was produced in advance of the mission to map the earth's gravity, and which has good and simple explanations within it. Also a great illustration showing the lumpy nature of earth.
It came as a surprise to me to realise that gravity wasn't uniform across the whole world. I remember my geography master at school treating with derision a book which suggested it wasn't, and that high mountains might have less gravitational pull than the plains. However, that's exactly what the article on the ESA site says.
There are a number of things which affect the strength of gravity. Apparently we weigh less at the equator than at the poles, because the shape of the earth is not truly spherical and bulges out in the middle, around the equator. As gravity weakens the further out from the middle of the earth you are, this makes gravitational force weaker where you are further from the centre.
There are other things which influence the gravitational force, including the composition of the earth's crust. Learning about the variations caused by those factors may help with tracking changes due to volcanic and earthquake activity.
Mapping the earth's geodesy, or shape, will allow scientists to calculate relative heights more easily, and to work out what influence the tides and currents are having on the shape of the oceans. It will allow more accurate measurement of relative heights, and provide much more accurate information about mountains and natural features.
It's very clever. As measurement of gravity gets more difficult at a distance, the Goce satellite has been travelling at the low level (for a satellite) of 250 km.