In AC circuits, most notably at frequencies where the transmission line is a significant part of a wavelength at that frequency, current may flow in one part of a circuit while not in another part of the same simple circuit. For example, in your sample the end of the transmission line is open circuit. At that precise point the current is zero. However, as we move a distance away from that point, back towards the generator, the current is no longer zero. The current amplitude begins to increase as we move away from that point. When we reach a distance of one quarter wavelength from that point, the current amplitude is at a maximum and begins to decline. So the current in this case has an amplitude along the line that is the shape of a sinusoid. This is so because you have a Standing Wave along your transmission line. In other words, the incident current going toward the end of the transmission line, and the reflected current coming back from that point, sum together and form a static pattern of amplitude that is this standing wave.
This would not be so in a DC circuit because DC current cannot flow across the open circuit at the end of the transmission line. But in AC, current can vary with distance along the transmission line because the current is flowing at nearly the speed of light.