Noble kava cultivars refers to varieties of kava deemed safe to drink daily. There are certain cultivars of kava, going by names such as "tudei" or "non-noble" where the kavalactone composition may cause adverse effects like nausea and vomiting among other things.
The kava market, for a long time, was littered with many kava products that contained non-noble kava, normally with a noble kava blended with a non-noble kava, to decrease production prices. Consequently, when people found out, many countries, mostly European ones, banned kava altogether. "Noble kava" was (and still is) a way for many vendors to make it clear that their product is 100% noble kava and contains no non-noble. Vanuatu, a major player in the kava game, has banned export of non-noble varieties, while these are still consumed domestically on certain items. The kava industry, at least what goes on in America, has gotten way better. If there are any kava vendors that sell tudei, they clearly label it as such. One of the varieties of tudei I know is being sold is called "isa," which has a composition that's considerably mellower than other tudei varieties, so it's less likely to make you sick if you treat it with respect.
When I mentioned "basal" and "lateral roots," these are different parts of the roots that have different strength and composition of the kavalactones, with lateral roots generally having a higher concentration of kavalactones. But, if I recall correctly, Fiji is the only country that does this. Other countries default to using all of the root. This is just to clarify for you since some vendors will talk about "lawena" (that is "basal roots") and "waka" ("lateral roots") in their products.
I'm no expert at all. Take what I said with salt since I, the human in me, can't keep all my details straight. I'm just a kava consumer, similar in class to most others around here. It took me a fair amount of time to learn about this magnificent plant and to learn what I like about it. The process will be easier if you hang around here. Lots of quality human beings gather here. They're here to help.