The terms left and right wing refer to the political spectrum, usually expressed in terms of a line with the far left at one end, the far right at the other and the centre in the middle.
In British politics, the Labour party are considered centre-left, with the Conservatives correspondingly centre-right. The Liberal Democrats occupy the centre, while UKIP are further right, and the Green party further left.
We can visualise these parties along the political spectrum like this:
(Left) Green party ---- Labour ---- Liberal Democrats ---- Conservative ---- UKIP (right)
The left and right wings differ on many things, but most importantly on the role of the state:
Left wing = believes the government should play an active role in regulating the economy and providing welfare (NHS, benefits).
Right wing = support a smaller state, with a greater role for the free market and business.