좋아요 is an adjective means that something is pleasant in your opinion.

좋아해요 is a verb that means "to like".

Some examples:

외국어를 배우는 것이 좋아요. (Learning foreign languages is pleasant.)

외국어를 배우는 것을 좋아해요. (I like to learn foreign languages.)

As you can see, because 좋아요 is an adjective, the thing being liked takes the subject marking particle (이/가) after it because you're just saying that "it" (subject) is pleasant to you.. Whereas in the case of 좋아해요, a verb, the thing being liked takes on the object marking particle (을/를) because you like "it" (object).