The short version: an argument is a logical structure in which a claim is explained by reasons which are supported by evidence.
Note that an arguable claim is distinct from both a preference (which is subjective) and a fact (which is verifiable).
Take the Red Sox as a subject. (It’s that time of year…).
“Jason Varitek is my favorite player” (I date myself here!) is a statement of preference; although others may disagree and we may fight about this statement, it is not arguable because I am entitled to my opinion and no amount of logic or evidence can sway me from my preference.
“Jason Varitek’s lifetime batting average was .259” is a statement of fact; you may not know whether the statement is true, and I may be wrong, but we can verify the statement (or find it not true) by checking record books or websites.
“On the defensive side of the bat, the most important player on a baseball team is the catcher” is an arguable claim; reasonable people may hold different opinions, and we can all (if we are baseball fans) summon reasons and evidence to suport our view.
See this page for discussion and examples of workable arguable claims.