In mesh analysis,currents are arbitrarily assumed and expressed in terms of KVL equations.By solving the unknowns,you were able to get the solutions.If it is negative then your assumed current were wrong,if not then it is correct.However,if you assumed the current arbitrarily,you might mistakenly modeled the circuit and so does the condition expressed in KVL equation.Despite being wrong you can still acquired the value of the current.How is that even possible? By modeling the circuit incorrectly you still solve the current?
Here is a nice overview of setting up the KVL equations and solutions obtained.
Here is a nice example of solving a 3 loop circuit:
If you solve a mesh circuit by arbitrarily assigning a current and it is in reality the wrong direction, for example, then the solution would show it to be negative if you got it wrong.
If the equations for KVL of all the loops are written correctly it will always work properly and give you the right solution set.
Let me know if you need more.