When people buy expensive items like cars and houses, they often borrow money from a bank to pay for them. However, they can't borrow all of it. They have to pay for part of it with their own money first. This money that you pay at the beginning is called a "down payment".
The verb "make" goes with "payment":
We've always made all our payments on time.
The preposition "on" labels the thing that you're paying for:
How many more payments do you have on your house?
I bought it three years ago, but I'm still making payments on it.
The payments that you make after your down payment are called "monthly payments":
The bigger your down payment, the lower your monthly payments will be.