These words are from Latin. "Emere" means to buy, so "redemption" is from the Latin for "buying back". "Burse-" is from Latin via French, and is cognate with Portuguese "bolsa" (English "purse"). "Re-" means back (as in "to return"), and "in" means "in" (or "into"), so "reimbursement" is literally "to put (money) back into the pocket / purse". To find out how these words are used in English, you can simply look them up in your favorite online dictionary.