I don't seem to be able to conceptualize this word "adventure". I checked its definition(s) in the dictionary but still don't clearly get its intended meaning(s). Is it something that you do for fun as in "the adventures of Mr. ABZ"? I'd appreciate your help.
An adventure is something more exciting than ordinary life. It usually involves some risk, or at least some unplanned encounters and challenges. Yes, it has a positive cast.
"The adventures of Mr ABZ" sounds like the title of a children's book to me. Those books are often about people who do some apparently ordinary things, that somehow turn out to be more interesting and gratifying than usual.
These are a couple of the common contexts in which you find the word. I suggest that you look search for "adventure" in context: Finding Examples in Context.
This will find you a wider range of examples of how it is used. If you have a question about a sentence you find, you can ask it here.