If you are solving a mixed-integer programming problem (any problem with integer constraints) with a non-zero value for the Integer Optimality % option in the Solver Options dialog, Solver has found a solution satisfying the constraints (including the integer constraints) where the relative difference of this solution’s objective value from the true optimal objective value does not exceed the Integer Optimality tolerance.  The solution on the worksheet may actually be the true integer optimal solution; however, Solver did not take the extra time to search all possible remaining subproblems to “prove optimality” for this solution.  If all subproblems were explored (which can happen even with a non-zero Integer Optimality setting in some models), Solver will produce the message “Solver found a solution.  All constraints are satisfied.”