Left-wing, right-wing and centre are very broad, one-dimesional terms to categorise people's political persuasions.
http://en.wikipedia.org/wiki/Left-right_politics
which although is also disputed
does give a decent outline of the myriad of ways people can be viewed as either extreme and the difficulties of labeling people as a result.
Most people are more left wing on some issues and more right wing on others, so personally I do find these terms often applied with laziness and used as a slight to another, which generally is not helpful to constructive debate. It often immediately brings out prejudices or sympathies if someone is classed as left or right wing, which I think is a poor reflection on our inability to address the subject matter on its own merits and look at the many shades of grey instead of black and white images to categorise positions.
For me the crux of the right wing/left wing political debate is the degree of government intervention, the extreme right wing being in favour of a complete free market with little government intervention, the left being the complete opposite; also, the right having the concept of the individual as the central focus, the left having collective socialism at its heart.
However, in reality, extreme right wingers often intefere a great deal more than idealogically they might be expected to; extreme left wingers creating a system that's unmanageable to the detriment of its socialist ideals. Sometimes the more extreme one side gets the more indistinguishable it becomes from the other extreme side....the National Socialist Party in Germany were a case in point.
As for the centre, I believe it refers to the combination of the two wings, but this is just as difficult to pin down. Many may see the Liberal Democrats as in the centre, yet others might say they are more left wing than the current Labour Party.
It is a good question to ask, but when looked at it should become clear the many inadequacies of using such terms.