Child sired by other than the husband, but accepted by both husband and sire.
In other words, mom went out and had a child by someone else but husband is okay with it. Doesn't happen a lot today (although I have heard instances of it happening) but I think it was a more common happening in traditional Hawai'i. A poʻolua child was lucky in the sense that it increased the number of relatives of the child (related to mom's family, dad's family, and biological father's family) and if he was aliʻi then it assured loyalty to him as kinsmen.
Poʻolua literally means "two heads" and the best example of a poʻolua child is Kamehameha I. His mother was Keku'iapoiwa and her husband was Keōuakupuapāikalaninui. Many historians believe that Keku'iapoiwa had a liaison with Kahekilinui'ahumanu (ruler of Maui) and from this union was born Kamehameha Pai'ea (otherwise known as Kamehameha the Great). Therefore, though Kahekili was thought to be his biological father, he was raised by his parents, Keku'iapoiwa and Keōua.
Now one must not frown upon this as being unacceptable behavior for Hawaiians. After all, they had a very intricate social system, practiced polygamy, had a matrilineal society and a monarchy. They had a very detailed kapu system. They had it all under control. All the fathers and mothers took responsibility for their offspring, cared for them, taught them.
He po'olua 'o Kamehameha I - Kamehameha I is a po'olua child