Learn Swedish: Veckan slutar på söndag.

In Swedish, the word for "the" isn't usually a separate word. Instead, it gets attached to the end of the noun. En vecka means "a week", and adding -n makes it veckan, meaning "the week".

Does slutar mean "ends" or "stops"?

It actually means both! In Swedish, slutar can be used when a period of time or an event concludes (like this week ending), and it is also used when someone stops doing an action.

Why isn't söndag capitalized here?

Unlike English, Swedish does not capitalize the days of the week, months of the year, or languages. So "Sunday" is always written in lowercase as söndag unless it is the very first word in a sentence.

If I wanted to say that weeks end on Sundays in general, would I still use på söndag?

If you mean "on Sundays" as a regular, repeating thing, you would use the plural form and say på söndagar. Using just på söndag typically means "on Sunday" (referring to a single Sunday).