The premise is a disagreement with the market, and it needs to be stated that way to be assessed. Buying a value stock means concluding that a price visible to everyone is too low. The seller on the other side of that trade has the same filings and the same price and has reached the opposite conclusion. So the position is not "this company is sound" but "the market has mispriced this company," which is a considerably stronger claim and the one that has to be right for the holding to work.
The value trap is the failure mode, and it is not a rare one. A price can be low because the market is wrong, or because the market has correctly noticed that earnings are shrinking, an industry is being displaced, or a balance sheet is strained. Both look identical on a screen that ranks by price against past earnings, because the screen reads yesterday's earnings and today's price. This is why measures that appear cheap can keep appearing cheap for years while the shares fall further, and why FINRA's caveat is the operative sentence rather than a disclaimer.
What "cheap" is measured against. In practice the screens use ratios that compare price with something the company produces or holds: earnings per share, book value, cash flow, or the dividend. Each has its own weaknesses and each belongs with its own term. The point that survives all of them is that every such ratio has the price on top, so a falling price makes a stock look cheaper on every one of them at exactly the moment the business may be deteriorating.
Contrarian investing is the deliberate version, and FINRA is explicit about what it takes. If you buy stocks that are out of fashion and sell stocks other investors are buying, FINRA says, you are a contrarian investor. It attaches a warning: "contrarian investing requires considerable experience and a strong tolerance for risk, since it may involve buying the stocks of companies that are in trouble and selling stocks of companies that other investors are favoring." Note what the tolerance is for. The difficulty is not analytical so much as behavioral, since the position is by construction unpopular and can stay unpopular for a long time.
There is no definition to look up. The SEC's investor glossary has no entry for it and FINRA describes it rather than setting a test. As with growth, what exists instead is the SEC's fund names rule, which treats "value" as a term suggesting an investment focus and requires a fund using it to adopt a policy of investing at least 80% of its assets in accordance with its own stated definition. So the definition sits in each fund's documents, and two honestly labeled value funds can screen on different measures and hold different companies. The mechanics of that rule are set out with growth stocks.
The portfolio question is separate. A broad market fund weighted by company size already holds these companies at the weight the market gives them. A dedicated value fund holds more of them than that, which is an active decision requiring an active reason.