It is likely an habitational surname, meaning it originated from a place name. The family likely lived near an oak tree or a place called "Cerna" (which could have been a village, town, or other geographical feature).
It's worth noting that the "de" part of the name is a preposition indicating origin, similar to "of" in English. So, it's not just "Oak", but rather "Of the Oak" indicating a connection to a specific place.