Residual in convergence plot represents if either the solution has converged or not. In solid mechanics, the solution is considered converged if the reaction forces in the system match the user applied forces under the user specified tolerance. This tolerance is what you normally give under Numerics for either absolute or relative convergence criteria.
So if you have set your relative error tolerance to 1e-6, than in one of the iteration if the relative error is reached until for example 1e-5 and the maximum iterations has been reached, than the solution will diverge and the timestep will cut down if Auto timestepping scheme was selected. On the hand, 0.9e-7 will lead to converged solution.
Hope this helps, If you have any further question/s, feel free to ask.