where does the brace height measurment come from?

From the string to the inner most part of the grip.

thank you. Having answered that, how does brace height affect shooting?

examples

30 inch draw length with a 8 inch brace height gives a 22 inch power stroke.

30 inch draw length with a 5 inch brace height gives a 25 inch power stroke.

The higher the brace height the more forgiving the bow because it has a shorter power stroke and the arrow gets off the string sooner.
Leaving less time for human error.

excellent definition. thanks....so then, does the shorter brace height equate to less speed?

Exact oppisite.

The lower the brace height the faster it would be.

The lower brace would give a longer power stroke thus making more speed