The word concubine (or its plural) is recorded 39 times in the KJV Old Testament. It is derived 36 times from the Hebrew pilegesh (Strong's Concordance #H6370) which means the same as its translated English word. The other three occurrences of concubines are in Daniel 5:2 - 3 and 23 where the original Aramaic word (Strong's #H3904) for the practice means the same as its English counterpart.
A concubine can perhaps be best understood in relation to polygamy. In a polygamous relationship, a man is married to more than one wife at the same time. A concubine, however, is the practice where a man who already has one or more wives takes on one or more females as his sexual partner in his household. Such women in the Bible were considered secondary wives or females of a lower status compared to a man's primary mate(s).
Why was it popular?
In the ancient world, the ability to support more than one wife or to possess both wives and concubines was a status symbol. Such an arrangement advertised not only a man's wealth but also was a sign of his virility, power and importance in society.
Who had them?
The rulers over God's people, like their pagan neighbors, collected multiple women for their use. King Saul had a concubine (2Samuel 3:7). King David had at least eight wives (2Samuel 3:2 - 5, 1Chronicles 3:1 - 4) and an unspecified number of concubines (2Samuel 5:13). Solomon maintained a mammoth harem of 1,000 women (1Kings 11:3) and his son King Rehoboam had 88 children produced through his massive household (2Chronicles 11:21). Other rulers also had a plethora of females at their disposal.
God's perfect will is that a man have only one mate at a time (Genesis 2:24, Matthew 19:1 - 9). The Lord, however, recognized the entrenched practice of possessing multiple women was due to the hardness of people's hearts. He therefore reluctantly, at Mount Sinai, gave laws governing it (Exodus 21:10 - 11, Deuteronomy 21:15 - 17) and did not outright forbid it for the majority of Israelites.
Two of the laws regulating a concubine or multiple wives are especially noteworthy. The first forbids any Israelite man, be they a king or average citizen, from marrying a non-Israelite. This law was meant to prevent God's people from being tempted to worship false gods and forsaking their Creator (Deuteronomy 7:1 - 4). The other law prohibits any human king over His people from having more than one woman at a time.
Nor shall he (Israel's king) multiply wives to himself, so that his heart does not turn away. Nor shall he greatly multiply silver and gold to himself (Deuteronomy 17:17, HBFV).
The treatment of a concubine and their offspring varied depending on a variety of circumstances. For example, Abraham was able to dismiss Hagar at the behest of Sarah his wife. Hagar's son Ishmael, produced with Abraham, was considered inferior to Isaac (Genesis 17:18 - 21, 21:9 - 14). On the other hand, the children produced through Jacob's concubines of Bilhah and Zilpah were consider of equal status with those produced through his wives Rachel and Leah (see Genesis 49).
Concubines were an accepted practice of Old Testament societies even though it was against God's perfect will. Its practice among first century Christians was non-existent, however, as it was clearly taught that a man should have only one wife (1Corinthians 7:2, 1Timothy 3:2, 12, Titus 1:6).