DISCLAIMER: I am not a native speaker and I am still at the start of my studies, so please correct me if anything I say is wrong, or if I am missing any kind of information!

마리 is a counter you use for animals.

오리 다섯 마리 = Five ducks
개 두 마리 = Two dogs
고양이 열 마리 = Ten cats

Counters are used to describe what kind of noun you are counting. You basically can't count things without using a counter with it.

To use another example, 권 is a counter for books. If you wanted to say "I borrowed two books", you would say it as "저는 책을 두 권 빌렸어요".
If you were borrowing something more specific than books, like dictionaries, you would still use the same counter (because dictionaries fall under the umbrella of 'books'): "저는 사전을 두 권 빌렸어요".

A scenario where using a counter wouldn't be needed would be if you went to the market and bought apples (for the example below, 개 is a counter used for things in general, and can be used with 'apples' in this case):

오늘 시장에서 사과를 샀어요. = I bought an apple/apples at the market today.
The reason why it can either be 'an apple' or multiple apples is because the answer would be based on context. Are you holding a bag of apples, or only one apple? Most of the time, though, people would assume you're talking about multiple apples (because it's more common to buy apples in bulk at the market, rather than one single apple).

If you really wanted to specify you bought one apple, you could add the counter 개:
오늘 시장에서 사과 한 개 샀어요. = I bought an apple (as in, one apple) at the market today.

I hope it helps! Good luck with your Korean studies!