So to understand how the stock market value is measured and understood you must start with the "what is the stock market?" question.
The stock market is all the publicly traded companies presenting their shares out there in a market for buying/selling. So any particular company will have a certain number of shares that any ol' person can buy or sell. That price for buying or selling is determined by how much other people are willing to buy or sell it.
We've established now how a single company's price is determined. So how is the stock market determined as a whole (or frankly a slice)? Well one way to do it is by how "large" a company is and to use that "size" as a proportional weight when looking at all the companies in the stock market. This "size" is called a market capitilization (or market cap) and is a measurement of all a company's outstanding shares multiplied by the share price.
So now you have the market cap and you're using it as a proportional weight, well what does that mean? Let's assume I open an index fund that will track all the companies in the stock market. And there are 10 companies in the stock market. Companies A, B, C, D, E, F, G, H, I, and J. And they have market caps that when broken down into percentages look like this (respectively), 20%, 15%, 13%, 11%, 9%, 8%, 7%, 6%, 6%, and 5%. Well I'm going to use that money in the index fund to buy an amount of shares from each company to maintain that percentage of concentration in my portfolio (the proportional weight). As the market changes I buy and sell appropriately. This is the basis behind an index fund, there are more complicated index funds but we're going to ignore them for now.
So how does that answer your basic question? Well a method of evaluating the stock market as a whole is to just look at a total market index fund (VTSAX for instance). Other people use the S&P 500 as their barometer as it generally tracks with the overall stock market (since it is the biggest 500 companies it generally drives the upward or downward movement of the market as a whole). And some people use the NASDAQ composite for their metric.
I hope this has helped a bit. :)