It is a graphical representation of the evolution of the optimization as a function of the number of individuals evaluated. The convergence history graph lets the you know how the optimization problem is converging to the optimal solution.
Let us suppose you are solving an optimization problem and you just put a long time for it to run. After some time you realize the problem is not converging and you need to stop and check what is going wrong. On the other hand, you might realize the problem has converged quite a lot and it is not converging anymore, so you might want to stop.
Clicking over the graph opens a bigger graph for easier visualization.