The story
From dividend + reinvestment + plan. From being a plan to buy more shares in the company which issued the dividend by using up the dividend, to reinvest in the company.
Etymology from Wiktionary, CC BY-SA 4.0.
dividend reinvestment plan
Today it means: A company-run program, in which for an enrolled shareholder, the program takes the company's stock dividend payout to the investor, to buy more shares in the company's stock. Full definition →