The coupon is set at issue and, on a plain fixed-rate bond, never changes. It is a percentage of par-value, so a 4.25% coupon on $1,000 of face pays $42.50 a year, split as $21.25 each half-year. The name comes from the paper coupons holders once clipped and mailed in.
Do not confuse the coupon with the yield. The coupon is fixed at issue; the current-yield and yield-to-maturity change every time the price moves. A 2% coupon bond issued in a low-rate year can yield 5% today simply because its price has fallen.
Example: a bond issued with a 2% coupon now trades at 72. The coupon still pays $20 per $1,000 a year, but you only paid $720, so your current yield is $20 / $720 = 2.78%, and your yield to maturity is higher still because of the pull to par.
Related: bond, par-value, current-yield, zero-coupon-bond, accrued-interest