What is an argument, and what obligation comes with "asserting" something?

An argument links statements to justify a validity-claim; and to assert something is to take on the duty to defend it with reasons when challenged.

Two linked ideas about how we reach knowledge:

• Asserting carries a duty. To "claim" (behaupten) something is implicitly to take on the obligation to defend it argumentatively if asked. You don't get to assert and then refuse to give grounds.
• An argument is a linkage of statements to justify a validity-claim (Geltungsanspruch) — either a claim about the truth of a state of affairs or about the normative rightness of an action.

So, in one line: to argue is to give reasons for or against a particular position. Arguments are the justifications or proofs you offer for an opinion or standpoint.

Tip: This is why "that's just my opinion" is a conversation-stopper, not a defence — asserting it already obligated you to be able to back it up.