Definition from Wiktionary, the free dictionary
To quote from Optimization in economics and finance 
- This terminal condition on λ(T) has often been called a transversality condition, for historical reasons deriving from time-optimal problems, where the (variable) time T to reach a target is minimized. In that situation, the transversality condition appears as a description of how the optimal path crosses a terminal line (graphing state against T).
- (economics) A terminal condition on a costate variable in a, usually infinite, time optimization problem.