Picture the stress strain graph right after the material crosses its yield point. In a linearly hardening plastic material, that graph does not flatten into a plateau, and it does not curve upward faster and faster either, it simply continues as a straight line with a constant slope. That constant slope behaviour is what the word linear means here, every extra unit of plastic strain adds a fixed extra amount of stress, following the relation stress equals yield stress plus a hardening modulus times plastic strain. Since the hardening modulus stays constant, the stress rises steadily and proportionally with strain, which means true stress increases linearly with true strain beyond yielding.