Learn Romanian: Bărbatul este aici.

In Romanian, the word for "the" isn't a separate word before the noun. Instead, it is added to the end of the word as a suffix. The base noun is bărbat (man), and we add -ul to make bărbatul (the man). The suffix -ul is the standard ending for masculine singular nouns.

Why is the verb form este used here?

Este is the "he/she/it is" form of the verb a fi (to be). Because the subject of the sentence is bărbatul (the man), which corresponds to "he", we use this third-person singular form.

Could I just say Este aici without the noun?

Yes! Romanian often drops the subject pronoun (like he, she, or it) when it is obvious from the context. If you and your listener already know you are talking about the man, you can just say Este aici, which translates to "He is here".

Is aici only used for location, or can it be used for direction?

You can use aici for both where something is (being here, like in this sentence) and where something is going (coming here). It works exactly like the English word "here".