Romanian has five cases, the details of them will be covered in much more depth over the course. As they are mentioned in the lesson briefly, here is a summary of what they are:
nominative: The most common case for a noun, the nominative is often the form listed in dictionaries. e.g. “they” in English is nominative.
accusative: The noun having something done to it. e.g.“them” is accusative. The sentence “They like them” demonstrates nominative and accusative.
genitive: This case shows possession, in English it's all that apostrophe stuff.
vocative Indicates the party being addressed. In the phrase “I don't know, John”, John is a vocative expression (I'm telling John I don't know). As opposed to the sentence “I don't know John” in which John is an individual I don't know.