“We're trying to save up so that we can afford a house.”

You go out to a restaurant with your friend and don't want to order much because you're saving money. You want to explain that you're saving because you want to buy a house. You say:

We're trying to save up so that we can afford a down payment on a house.

save up

This means to save money and build it for a certain purpose, like buying a house or car.

(do something) so that (clause)

The structure "___ so that ___" explains your reasons for doing something.

I'm trying to be quiet so that the baby doesn't wake up.

In normal spoken English, you can drop "that":

I'm trying to be quiet so the baby doesn't wake up.

But it's not strange to leave "that" in, even in casual conversation, as long as you don't stress that word.

afford (something)

This means to have enough money to buy something:

We can't afford to send our kids to private school.

To "afford" something isn't an action like "run", "buy", or "think". It's a state, like "need" or "have".

a down payment on (something)

A "down payment" is the money that you pay at the beginning when you are taking out a loan to buy something big like a house. Even though you are borrowing money, you still have to pay some money at the beginning to show that you are serious about buying 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.