What people want to pay = the market
The total market capitalization = the value of the company.
When people on Bloomberg/CNBC/whatever say things like "this is a 100 Billion dollar company", they're talking about MARKET CAP value.
Take these two stocks I found using a stock screener:
FTR - SEC reported data
Shares outstanding: 995 million
Total assets: $17.461 billion
Total liabilities: $13.006 billion
Book value: $4.455 billion
ZION - SEC reported data
Shares outstanding: 185 million
Total assets: $53.149 billion
Total liabilities: $46.164 billion
Book value: $6.982 billion
So which company has a higher value? Looking at the reported book value (assets minus liabilities), it looks like ZION is by about 50%. But when you go to buy a stock, you're not paying the company based on the difference of their liabilities and assets, you have to pay someone in the market who already has shares and is willing to sell them to you for a fair price. We need to see what the market price is, but it isn't in the SEC filings... so let's look at the price per share on the market.
FTR price per share: $3.99
ZION price per share: $21.24
Now which is worth more? Is the company ZION as a whole worth 6x more because of the price per share? No, because we still don't know the total market cap, so we need to multiply by outstanding shares.
FTP market cap: $3.99 * 995,000,000 = $3,970,000,000
ZION market cap: $21.24 * 185,000,000 = $3,929,000,000
Wait a second - they're almost exactly the same! In fact, FTR has a slightly higher market cap - meaning the market values the company slightly higher than ZION, despite the difference in assets and book value. THESE COMPANIES ARE WORTH ALMOST EXACTLY THE SAME, even though the SEC data is wildly different between the two. It has nothing to do with what the company tells the SEC, it has everything to do with how much the market is willing to pay for the company, usually based on earnings potential and growth rates. If the SEC filing dictated the value of the company, all stocks would trade at the same multiple of "book value", which we can clearly see isn't the case here.
Note: I screened these two stocks using market cap (searched for $4BB companies) - Google finance defines "market cap" thusly: "Market capitalization is the total value of a company in the stock market. It is calculated by multiplying total shares outstanding by the current price per share."