A "whale" is an address (or an investor) that concentrates a significant share of a cryptocurrency's circulating supply — large enough that a single sale or trade can move the price noticeably.
Why their moves are watched
Since these markets have less liquidity than major traditional stock markets, on-chain tracking tools let you see in real time when a whale moves funds to an exchange (a possible sign of an upcoming sale) or withdraws them to a cold wallet (a possible sign it plans to hold long term).
The concentration risk
When a handful of wallets control a large share of a token's supply, there's a higher risk of price manipulation and sharp drops if those whales decide to sell in a coordinated or sudden way. Checking how a token's supply is distributed is a routine part of applying DYOR before investing.
Not exclusive to cryptocurrencies
The term is also used, less often, in traditional markets to refer to large funds or institutional investors whose trades can move the price of a thinly traded stock.