A discount variable rate is where you get a discount from a lender's standard variable rate (SVR) – which is just their boring old normal rate. As simple as that.
It’s somewhat common in mortgages, where you might get a discounted variable rate for a set period of time at the start of the mortgage as an offer to entice you in. After that you would move onto the lenders standard variable rate without a discount.
You might be able to remortgage to a better rate after the lower discounted rate period ends. Learn more about mortgages and remortgaging.