First try checking the streamline box. The red line that appears is a streamline passing through the origin. Note that streamlines are lines that are everywhere tangent to the velocity vectors. You can see this more easily by pressing the stop button.
Now try checking the pathline box. A pathline is a line that a single fluid particle traces out over time. It's the line that one would get from a long exposure photograph highlighting a single fluid particle. You can produce a pathline for a fluid particle leaving the origin by moving the mouse cursor into the flow field and pressing the mouse button. This will release a fluid particle and show the corresponding pathline as a green line. Notice that the streamline and pathline are not necessarily the same line.
Now try checking the streakline box. A streakline is a line connecting all the fluid particles that have passed through a common point. It's the line one would get if dye was released from a particular location in a flow field. The streakline will appear as a blue line that passes through the origin. It is the line that one would get if fluid particles were released one after the other. Try releasing another fluid particle (by moving into the flow field and clicking the mouse button) and notice how the fluid particle follows both the streakline and the pathline.
In an unsteady flow, the three common forms of flow visualization: streamlines, streaklines, and pathlines are not necessarily the same. In a steady flow, however, all three lines coincide.