Why bond-equivalent yield exists
Some short-term instruments are quoted on a bank discount basis that uses face value rather than purchase price in the denominator and a 360-day convention rather than a 365-day year. Those conventions are useful for quoting bills, but they can understate the investor's effective return when you compare them with other yield measures.
Bond-equivalent yield adjusts the short-term return onto a price-based 365-day annualized basis. That makes the result easier to compare with coupon-bond yields and other annualized fixed-income metrics.