Accrued interest is the amount that the bondholder is supposed to get from the bond issuer, but it is yet to be paid. If the present bondholder sells his Bond before maturity, he has to get the interest accrued until the date of sale.
There can be a time gap between the last interest payout made to the bondholder received until the date he/she sells it since, the next interest payout goes to the buyer/ new bondholder, the buyer must pay this accrued interest to the seller/ previous bondholder, along with the selling price of the Bond.
The settlement amount is the amount the buyer has to pay to own the bonds. The settlement amount is the sum of the market price of the Bond and accrued interest.