"formal declaration of sympathy," 1670s, pl. of condolence. Reason for the plural is unclear; earliest references are to expressions from groups of persons; perhaps the habit stuck.

condole (v.)
late 15c., "to sorrow," from L.L. condolere "to suffer with another," from com- "with" (see com-) + dolere "to grieve." Meaning "to express condolences" is recorded from 1650s.

"Condolences" feels like such a formal word these days, but at its heart it doesn't just mean: "I pity your sorrow from afar." It means: "I suffer with you."