It's the length of time it takes the person to say their line.

ie. Touga says: "Certainly, she is engaged to you currently. However, that doesn't mean you can do whatever you please to her." Miki then stops his watch at the end of Touga's line. The time on his watch should be the same as the time it took Touga to say that preceeding line.

(I don't remember if Miki actually stops his watch there, though, but I hope this clears up the idea.)

Nessy wrote:

Wait, so according to Ikuhara the stopwatch says the time between the last line that was said and the next line said?
Or it says the time between the clicking and the line right before it?

I am so confused.

From what I watched on the Youtube SKU series and when I checked the time on the stopwatch and I went back the number of seconds that the watch displayed and it goes back to the beginning of a key moment.