Care to explain "Live Timing" from Moto GP site?

I am watching the "live timing" site on the Moto GP website.

I would like to know how timing works exactly, I see for instance "Best Lap"
which is self explanatory, but when I see "Lap" and it has 64/65 does this
mean that the rider rode 65 laps and did his best time on the 64th?

If so, then if this rider did 65 laps and his last lap time is significantly
slower than the 64th lap, was this a cool down lap? Why so much discrepancy
in the number of laps run, and when watching the live timing, what does the
highlighted bar on each of the riders names mean when it comes up?

Just trying to learn, thanks.

 

Well, I feel a bit of an idiot here, as the more I watched the more I
understood. BUT, can someone still explain to me how the timing is
generally run? Right now for instance, I see that Caprirossi has run
something like 21 laps, Hopkins is at 85. What is this about?