A trough is an extension of a low-pressure centre visible as a cyclonic curvature of isobars (or contours aloft). It represents an axis of relatively lower pressure without forming a closed low.
Forecasting importance
Upper-level troughs are the main generators of instability at mid-latitudes. Ahead of a trough, dynamic lifting (upper-level divergence) promotes cloud and precipitation formation. DANAs (cut-off lows) are troughs that have detached from the main jet stream flow. Its opposite is the ridge.