Living together with several different sex/romantic partners. To have multiple girlfriends or wives, all of whom know about each other and live in the same house. Polygamy.
Originated thousands of years ago as a means of producing a large number of offspring, and as a status symbol, to show off how many women and children a man could afford to provide for, and to display virility. Now banned in most countries, but was once common practice, even in early Christendom: Charlamagne had multiple wives.
The word was recently popularized by one Ricky Lackey, a convicted thief who, when asked by the judge at his trial how many children he had, replied: "None now, but I have six on the way." When the judge asked if he was marrying a woman who had six children, he replied "No, I be concubining." Meaning, of course, that he had 6 girlfriends, all of whom were pregnant.
Judge: "Do you have any children?"
Lackey: "No, but I have six on the way."
Judge: "So, you're marrying a woman with six children?"
Lackey: "No, I be concubining."