What does it mean to say a deductive argument is "sound"?

A sound deductive argument satisfies the two criteria of being both a) valid and b) having all true premises.

Determining soundness requires both a logical task of determining validity and the task of determining the truth of the premises (carried out, presumably, by whatever field is concerned with the subject matter of those premises).

An argument may be "unsound" if it fails on either a) or b) above (or, of course, both).
 

There are several reasons why logicians restrict their attention to validity:

First, determining the truth of the premises requires determining the meaning of the sentences in which the argument is expressed. This is always open to "interpretation" and thus cannot always be decided unarbitrarily. Logicians cut through all of this by asking, if the premises turn our to be true, what then?

Second, we often want to reason "hypothetically" from assumptions the truth value of which is unknown, as a way of deciding whether the premises are true or false, or whether or not, if they concern matters under human control, to make them true or false.

Third, we may want to reason "contrary to fact" from premises known to be false as a way of deciding what could have been true had other conditions prevailed.