A couple means two, but in reality "a couple of days ago" could be any time within the last week or two.

What does your dictionary give? The dictionaries that I checked were helpful. Oxford Learners Dictionaries https://www.oxfordlearnersdictionaries.com/definition/english/couple_1?q=couple couple determiner BrE /ˈkʌpl/ ; NAmE /ˈkʌpl/ (North American English, informal) ​used before plural nouns to mean ‘a small number of’ or ‘a few’ synonym a few It's only a couple blocks away. Collins Dictionary https://www.collinsdictionary.com/dictionary/english/couple quantifier If you refer to a couple of people or things, you mean two or approximately two of them, although the exact number is not important or you are not sure of it. Across the street from me there are a couple of police officers standing guard. [+ of] I think the trouble will clear up in a couple of days. [+ of] ...a small town a couple of hundred miles from New York City. [+ of] Couple is also a determiner in spoken American English, and before 'more' and 'less'. ...a couple weeks before the election. I think I can play maybe for a couple more years. Couple is also a pronoun. I've got a couple that don't look too bad.

A “couple” is two but people in the US use this term loosely so it could be more than two. If it’s important, you should clarify if the person really means two.

To my understanding is something like three to four days

In the community where I grew up, "it's a couple of ..." always means "I think it's about two ..." - So it's a loose way to say "probably two, but it might be a little more". We always use it to mean two. Why say "a couple" instead of "two"? Because I'm not 100% sure it's two, it could be three or possibly four. If we believe it's 3 or a little more, we say "a few". I think this might not be used the same way in different communities.