Stock Index & Indicies

I couldn't find anything pertaining to this anywhere in the forums, at least in English, so.. here goes.

Been poking around the stock market and looking at the different lists and such. I have noticed there are the stock markets (Frankfurt, Tokyo, New York), and certain countries go to certain stock markets, but I am curious what the indices mean. I had thought, based on real life models, the indices were a cross-section of the "core" companies available on each exchange.

However, it seems very few current stocks are on the indices right now. Are there advantages/disadvantages to being on a stock index? Is there a reason some are on there but most are not?

The indices are only generated every week.

The ASIX20 lists the top 20 enterprises regarding market value.

Regional indices list more enterprises with high market values - the NAXX (with North American enterprises only) lists the top 30, other regional indices list fewer enterprises. Enterprises, that are already listed in ASIX20 are not listed again.

The stock exchanges list all enterprise stock of a certain region.