Soundness is a logical concept, and when a philosopher uses the word, she means the logical concept. Soundness is not a property of a statement, but that of an argument. An argument is defined as a set of statements where one statement is a conclusion and all the others are viewed as premises (or assumptions). An argument is staged to show that the conclusion of the argument has to be true. For this, an argument must be both valid and sound. By definition, an argument is valid when it is logically impossible for all its premises to be true and its conclusion to be false, In other words, if all its premises are true, in a valid argument, the conclusion must be true. Also by definition, an argument is sound when it is valid and all its premises are true. Ergo, the conclusion of a sound argument is always true. For this reason, soundness is the ultimate virtue of an argument. (By the way, the above material is taught in any intro to logic course).
Philosophers draw different, sometimes, conflicting, conclusions, because they disagree on the truth of some of the premises. For example, pro-choice theorists tend to assume that a fetus is not a person, and more like a tumor. To establish this assumption, they might appeal to the fact that both tumor and fetus share similar aspects (unwanted, growing big, hindering the ability of moving around freely). Once establishing the identity (fetus = tumor), they can conclude that it is morally permissible to remove a fetus from one's body. Pro-life theorists, by contrast, assume that a fetus is a person. To prove this assumption, they will try to appeal to the fact that human society and culture have treated a fetus like a baby. Once establishing the identity (fetus = baby), they can conclude that it is morally impermissible to kill a fetus since it is morally impermissible to kill a baby.
As issues surrounding abortion arguments show, all the heavy lifting is done through establishing the truth of the premises (no philosopher proper would make a mistake in the validity of an argument), which is nothing but showing the soundness of the argument.
