A salt wife is a bound concubine in ironborn culture, usually the women kidnapped during raids. An ironborn man may keep as many salt wives as he can support, but at any one time he may have only one "rock wife", who must be of ironborn origin.
Salt wives have a low status in ironborn society, similar to thralls. They do not toil in the fields and mines as thralls do, but they do serve as concubines in all but name.
In some ways, salt wives are the opposite of paramours kept in Dorne: Dornish paramours are relationships based on love, and which are often marriages in all but name. Paramours occupy high-ranking and respected positions in Dorne, but children born to paramours are still considered bastards. In contrast, salt wives have a low-ranking postion in ironborn society, but children born to salt wives are not considered bastards, though they do rank behind the children of a man's rock wife in the line of succession (even if they are older).
In the books
A salt wife isn't quite the same thing as a slave, as even the ironborn don't believe in "slavery" as such. The main difference is that salt wives cannot be bought, sold, or traded: an ironborn man may only keep the salt wives that he has personally captured in raids, as this is considered "paying the iron price". Also, the ironborn generally look down on selling slaves, as they still think of their captives and thralls as human beings, albeit on the bottom rung of society, and not animals to be sold.
Salt wives are a somewhat unique cultural phenomenon among the ironborn: they are actually considered to be "married" to the man, as their union is solemnized by a priest of the Drowned God. Technically, this places them a step above actual label of "concubines" - though most are treated as little more than concubines. The ironborn don't consider this to be an instance of "polygamy" either, as a salt wife is a different kind of realtionship than a "rock wife", which a man may only have one of at any given time.
The children of salt wives are explicitly not considered to be bastards, and they use their father's surname. If baptised in the faith of the Drowned God, they are even considered ironborn. However, they rank behind a man's children by his rock wife in the line of succession - much as the low-ranking fifth son of a lord isn't considered as prestigious as his eldest son and heir. While not officially disparaged culturally, those descended from salt wives can still sometimes bear a stigma: For example, after Dalton Greyjoy was killed at the end of the Dance of the Dragons, the Iron Islands were plunged into civil war, because he had never taken a rock wife and only had sons by his salt wives. Other Greyjoy cousins felt they had better claims as the sons of rock wives, and Dalton's sons also squabbled among themselves given that there was more than one "eldest son", one from each salt wife, each of whom felt they had a better claim.