All the factors about a specific business that an investor might use in deciding whether to invest. These include its profitability, the strength of its balance sheet, the acumen of its management, the prospects of its industry and so forth. These factors generally would not include the current state of the stock market.
If religious fundamentalists might be said to learn everything they need to know from the Bible, stock fundamentalists learned everything they need to know from ""Security Analysis,"" a landmark book by Benjamin Graham and David Dodd. There are other such books, of course, and endless refinements, but the principals are the same: to discover stocks whose inherent soundness is undervalued by the market. Fundamental analysis need not be complicated; basic ratios such as price/earnings, debt/equity and the quick ratio can be easily derived from a company's financial reports, and are especially telling when compared to the same figures for other firms in the same industry.
Fundamental investors also tend to seek firms whose management owns a significant stake, firms in businesses that others can't easily enter, firms in businesses that aren't heavily regulated, and firms in businesses that are easily understood and not continually roiled by technological change.
Investors who emphasize fundamentals are often known as value investors. Warren Buffett is among the most famous.