Following are some definitions from CLRS:
1. Cut (S ,V-S) : of an undirected graph G = (V,E) is a partition of V(as defined in CLRS Book) .You can think it as a line that divides graph into two disjoint sets of vertices on its either side.
2. Light edge:Any edge crossing a cut is light edge if its weight is the minimum of all the edge crossing the cut.Light edge is defined with respect to a particular Cut.
3. A cut Respects a set A of edges if no edge in A crosses the cut.
4. Safe edge is the edge which we can add to MST without any violation of MST's property.These are those edges which are the part of final MST.