When the free ends of a tester are dipped into a solution, the magnetic needle shows deflection. Can you explain the reason?

The magnetic needle shows deflection because of the conduction of electricity through the free ends of the tester. Here, the current will flow only when the circuit is complete, that is, when the solution allows electric current to pass through it. So, here, the deflection of the magnetic needle indicates that the given solution is conducting in nature.