s-t Cut

An $s$-$t$ cut is a cut where $s \in S$ and $t \in T$. It separates the source from the sink. The source and sink are forced to opposite sides of the partition. Every flow from $s$ to $t$ must cross this cut. If you remove all edges crossing the cut, no flow can reach $t$ from $s$.

The cut acts as a barrier. The value of the cut is the total capacity of edges leaving $S$. This represents the maximum flow that can cross the cut from the source side to the sink side.