A trough is an extension of isobars from a low pressure area in the surface levels. It is defined as an elongated region of relatively low atmospheric pressure, often associated with weather systems.
Along a trough line winds rotate in an anti-clock direction. A trough is represented by a line between two opposing winds. If we join all the points where maximum turning of winds take place, we will get a trough.
A trough denotes bad weather in terms of clouding and rain/thundershowers. In fact a trough is always associated with some weather activity either directly or indirectly. The opposite of a trough is called a ridge, which denotes fair weather. Ridge is an extension from a high pressure area.
The image above shows a North-South trough in the Northern Hemisphere.