Big-time investors can influence the market in a big way. People follow their moves or attempt to predict where they're going in order to get in ahead of them. Think of it like a famous athlete with an endorsement. Steph Curry might get you to buy Under Armour. Warren Buffett might get you to buy shares of Coca-Cola.
If Warren Buffett wants to own 15% of a company, but word leaks he's buying at $30 and owns 5% of the company now...the next day the stock will shoot to $35, and he won't be able to finish buying what he wanted to buy at the price he desired. So he...anonymizes. Thus, these investors sometimes look to disguise their participation in certain trades. To do this, the investors can engage in anonymous trading, which keeps their involvement secret.
The trade itself can't be kept away from the public eye (a large transfer of shares on a public exchange makes a splash) but anonymous trading keeps the identity of the person making the transaction under wraps.
