What is the difference between saying, "Ho incontrato una persona" and "Ho conosciuto una persona"?
I'm trying to say that I met a person, not in the sense that we had planned a time to meet, but that I happened to meet this person by chance.
Ho conosciuto means that you and that person were introduced to each other, or just began chatting or whatever, and now you know their name, will recognise them if you meet again and so on.
Similarly, “have you met XXX?” translates more or less to conosci XXX?
The verb incontrare is more generic, and convey the notion of meeting someone, either by chance or deliberately, whether you already know them or not. A good description (in Italian) of its uses, with lots of examples, is here.