In a regular bond, a company or government borrows money from the market in exchange for a promise to pay the money back with interest at a fixed time. In a green bond, a company or government borrows money from the market in exchange for (1) a promise to pay the money back with interest at a fixed time and (2) a promise to do green stuff with the money. “Do green stuff with the money” means essentially a commitment to spending the proceeds of green bond issuance on projects with a positive environmental impact (renewable energy, clean transportation, environmentally sensitive land and water management, etc.); there are some international norms about how it works.
From first principles, green bonds should only exist (and they do exist) if they are worth more than regular bonds with the same economic terms. That is, if a company or country could sell a 10-year bond with a 4% coupon for $100, then it should be able to sell a 10-year green bond with a 4% coupon for, like, $101. From the issuer’s perspective, the green bond limits its flexibility—the issuer has to make more promises than in a regular bond—so it shouldn’t issue a green bond unless it can get more money for it. From the investors’ perspective, presumably they want the extra promises of the green bond; they are buying it not just for a financial return but also because they care about the environment. So they should accept a lower financial return in exchange for getting more of the other thing they want.