On opening the applet, every molecule has the same speed (but random direction) so the initial "speed distribution" is just a spike at that speed. Elastic collisions between molecules rapidly change the speed distribution towards that predicted by Maxwell, discussed in detail in my lecture.
In the right panel, the top speed distribution is an instantaneous reading, the other the average over time. Of course, Maxwell's distribution was for molecules in 3D, we're only in 2D, but the identical statistical argument works, the only significant difference being that at the low energy end, the 3D distribution begins parabolically, the 2D linearly.
Click to see the "Theoretical" (2D) curve (as predicted by Maxwell). This also gives some idea of the fluctuations, Explore how the fluctuations vary with the number of particles: much more pronounced (as a fraction of average value) for 100 particles than for 1000. Use the Pause button a few times to get a clearer picture of the magnitude of the fluctuations.