I have run android CTS test case for ics on custom board. AOSP had their own cts/ folder under android/ folder. I'm having two questions.
What is the use/role of cts/ in building and flashing android on board?
Why we download CTS from site to run cts test cases, instead of using source code's cts?
For your first question, CTS doesn't play any big roles in flashing android onto a device. It gets included with the build when you repo sync so it stays synced with your version of android.
As for why you download it off the site, there's 2 good reasons. One, most people who run or execute CTS are not interested in downloading, and building, an extremely large project just to make sure their device is compliant with that version of the android sdk.
Two, the CTS package you get off the site is what is going to be run by everyone, and not the CTS that gets built from your machine. If you create an AOSP fork, the the person who uses your ROM will still want to make sure that it is CTS compliant. They need to use the package from the site because they need to know it hasn't been tampered with. You could easily change CTS so your device passes your version of CTS, but that doesn't help anyone else.