This won't be the best explanation and I'd appreciate it as well if someone replied to this post since it's something I struggle understanding as well, but this is what I've been able to kind of settle on so far. I'd love it if people pointed out where the mistakes are.
Liability means a sort of obligation or debt that you have, so in terms of economic sense it is when you have a debt you are required to pay off.
Due to a small population alongside a small household saving ratio Australia as an economy always runs on a current account deficit since we can't raise enough capital from our own population and we require loans. These net external debt and equity borrowings add up to make our Net Foreign Liabilities. (Essentially what we have borrowed and are now liable for.)
Net Foreign Liabilities are made up of Gross Foreign Liabilities - Gross Foreign Assets.
Pretty much imagine the Net Foreign Liabilities to be the REAL amount that you are required to pay back whilst the Gross Foreign Liabilities is the TOTAL amount, Now the reason you don't pay back the total amount is because the borrowed money was an investment which was used to purchase assets, something you're not liable for, so from the the Gross Amount of Liabilities you subtract the amount of Gross Foreign Assets and you're left with the REAL amount you are required to pay back.