It's talking about something related to the topic.. too much! You don't need to give so many details about our or tell a story about what happened or give your opinion about it.. you should go back to the main topic:. You say, Oh, .. I went off on a tangent there.

Of course, this noun is first and foremost a math term. It is also used, as you said, to describe a person who makes a sharp or sudden change in their course of action or speech. For example, "my friend really flew off on a tangent when his girlfriend mentioned marriage". The word can be used as an adjective. For example, "my friend presented a lot of arguments tangential to the main point but they had little relevance". Another example might be, "his worries about the cost of an engagement ring were tangential (or incidental) to the discussion of whether they should get married". Hope this helps

Usually when people "go off on a tangent" it means that they got distracted from the original story or conversation by some irrelevant detail. For example if we were talking about your walk through the park and you mentioned seeing dogs and I got distracted talking about how much I love dogs then I went "off on a tangent".

Usually, they are on a tangent when they talk about something which is only vaguely connected to the original topic of discussion

Does it mean a person keeps changing the topics while talking to that person?