What is a trough?

A trough on a mean sea level pressure chart, (or an upper air contour chart) can be picked out by an arrangement of isobars (contours) which are concave towards an area of low pressure (low contour height) along a particular axis, and that axis is defined so as to lie along the points of maximum curvature on the individual isobars (contours).

If this sounds complicated, it isn't really: the feature is analogous to the 'valley' on an OS map and defined in the same way - pressure, or contour heights 'fall' into the trough line. A front may have troughing along its length, but not all troughs are frontal! Indeed, not all troughs have 'weather' associated with them in the cloud/rainfall sense. Lee troughs found downwind of a major range of hills/mountains are often cloudless, and thermal troughs forming over land during the day due to mesoscale heating may only be found by careful drawing of isobars: if the air is dry and/or stable, little significant cloud will be associated with this feature.

A modern complication on charts used on the GTS is that plumes of high humidity...e.g. in the case of very humid/warm air coming northward out of France/Iberia, are also shown as 'trough' lines for want of any other identifier. Although with development pressure may become lower along this 'plume' than surrounding areas, and therefore qualify as a trough by the above definition, often the difference is small or initially non-existent.