Current yield answers one narrow question: what cash income does this bond throw off per dollar invested right now? It is the bond equivalent of a dividend yield on a stock.
It is useful for income comparisons and misleading for total return, because it completely ignores the pull to par-value. On a premium-bond it overstates your return; on a discount-bond it understates it.
Example: a bond with a 6% coupon trading at 120 has a current yield of $60 / $1,200 = 5.0%. But if it matures in four years you will also lose $200 of price, so the yield-to-maturity is closer to 0.9%.
Related: yield-to-maturity, running-yield, coupon, premium-bond