Protons have positive charge on them. Protons aren't mobile. So how can a positive test charge move from the negative terminal of a cell to the positive terminal and gain electric potential energy? Why does negative charge not move from the negative terminal to the positive terminal? Electrons flow in a circuit, and electrons have negative charge on them so why is it said that positive test charge moves from the negative terminal to the positive terminal? Please explain.
When the idea of electricity was discovered, it wasn't known that there were atoms, and that there were electrons that could move around. Since the definition of electric charge is completely arbitrary (we just need to opposite charges, doesn't really matter which is which) they figured that it was the positive charge that flows through the circuit.
That's why in circuit diagrams the direction of the arrow indicates the direction of flow of positive charge. But saying a positive charge is flowing from left to right is the same as saying a negative charge is flowing from right to left. Hence one differentiates between the directions of "conventional current" (flow of positive charge) and "real current" (flow of negative charge). This distinction is never actually made in practice, but it's good to keep in mind while looking at circuits.
Also, I should point out that positive charge does actually flow in the case of electrolytic reactions, when the conducting medium is a solution (like sodium chloride) where the atoms get ionized and ions of positive charges flow in one direction and ions of negative charges flow in the other direction.