A single pair tells you about two currencies at once and cannot separate them. If EUR/USD rises, either the euro strengthened or the dollar weakened, and the pair cannot say which. A basket index answers that, which is why central banks publish trade-weighted measures and why traders check one before concluding anything about a single currency.
Baskets differ in construction. The widely quoted dxy uses a fixed set of six currencies with weights dating to the 1970s, so the euro dominates it and China is absent entirely. The Federal Reserve's broad index is reweighted to actual trade shares and behaves noticeably differently in periods when Asian currencies move.
Adjusting for inflation turns a nominal index into the real-effective-exchange-rate, which is the version used for competitiveness judgements.
Example: the dollar rises 2% against the euro but falls 3% against the yen, 2% against the yuan and 1% against the Canadian dollar. A euro-heavy index shows dollar strength; a trade-weighted one shows dollar weakness.
Related: dxy, real-effective-exchange-rate, currency-correlation, appreciation