Hold a 5-year bond for a year on an unchanged curve and it becomes a 4-year bond, repriced at the lower 4-year yield. Lower yield means higher price, and that gain is roll-down. Add it to carry-fixed-income and you get the total return of standing still.
Roll-down is largest where the curve is steepest, which is why traders hunt for the steepest segment rather than simply buying the highest yield.
Example: the 5-year yields 4.20% and the 4-year 3.95%. After one year the bond is repriced 25 bp lower. With duration near 3.8, that is about 0.95% of price gain on top of the 4.20% coupon.
Related: carry-fixed-income, normal-yield-curve, flat-yield-curve, forward-rate, duration