Buy-Up
A "buy-up" can be an underage person asking an of-age person to buy them alcohol...or a mortgage term.
For a mortgage, a buy-up is a rebate used to alter interest rates and closing costs on the loan from what was originally offered.
People usually think just their credit score determines their interest rate and closing costs on a mortgage, but actually, the buyer can purchase rebate points to lower their closing costs, and take a higher interest rate (and higher monthly payments). Each point purchased is typically worth about a quarter of a percentage point off the interest rate. The bank pays the mortgage broker, or the borrower (it depends on the terms) a rebate amount at closing, which lowers the closing costs. When it goes directly to the broker, it's referred to as a yield spread premium (YSP), and is part of their fee (commission).
Volunteering for higher interest rates seems contradictory, but it makes sense for people who don't intend to own the home the full term of the loan, or those who want extra money right away at move-in for renovations.
On the other side, mortgages also offer a buy-down. This is the buyer trying to lower the interest rates for a period of years, or even the whole loan, with the help of the seller. In this case, the seller puts money into escrow to make payments alongside the buyer and lower the buyer's portion of payments. Might also sound odd, but it can be done as a way to sweeten the deal on a hard-to-move home, or in a slow real estate market. This method lowers the monthly payment, which makes it easier for the buyer to qualify for the loan.
Say you're selling a fixer-upper...there's a lot of "fixer" involved, and it's scaring buyers away. But you really, really need to sell in order to relocate for work. You could offer this buy-down as a way of giving the buyer a lower payment, so they have more money available to renovate. It'll cost you a bit to put the money into escrow, but it's better than being tied to the house, so you go for it.