0. Who is paying whom, what, and why?
Imagine you bought a bond from someone:
Seller: They have held the bond for the last 00 days and are entitled to interest for that period. However, since the interest payment date has not yet arrived, they have not yet received this money from the bank/government.
Buyer: You are buying the bond today. When the next interest payment date arrives (i.e., when 000 days have passed), the bank will pay the entire 0 months' interest to you alone.
Problem: You will receive the full 0 months' interest, but you will have only held the bond for the last 000 days (000-00). The seller's 00 days of labor will go into your pocket.
Solution: To avoid any injustice, when you buy the bond, you should pay the seller: "Brother, you held this bond for 00 days and earned the interest. The bank will make a lump sum payment to me in 0 months, so I'll pay you the $00.00 you're entitled to now in cash," you say.
Summary: The buyer pays the seller the "accumulated interest" in cash.