0. Solver found a solution. All constraints and optimality conditions are satisfied.

This means that the Solver has found the optimal or "best" solution under the circumstances. The exact meaning depends on whether you are solving a linear, nonlinear, or integer programming problem:

If you are solving a linear programming problem with no integer constraints, the Simplex Solver has found the globally optimal solution: There is no other solution satisfying the constraints which has a better value for the objective (Target Cell). It is possible that there are other solutions with the same objective value, but all such solutions are linear combinations of the current decision variable values.

If you are solving a nonlinear programming problem with no integer constraints, the GRG Solver has found a locally optimal solution: There is no other set of values for the decision variables close to the current values and satisfying the constraints which yields a better value for the objective (Target Cell). In general, there may be other sets of values for the variables, far away from the current values, which yield better values for the objective.

If you are solving a mixed-integer programming problem (any problem with integer constraints), the Solver has found a solution which was within the range of the true integer optimal solution allowed by the Tolerance value in the Solver Options dialog (5% by default). If the problem is linear or quadratic, the true integer optimal solution (within the Tolerance) has been found. If the problem is nonlinear, the Branch & Bound process has found the best of the locally optimal solutions found for subproblems by the GRG method.