Hi Jessica,
"Runneth" is an archaic (no longer in use) form of the verb "run".
It is believed that the ending - eth (used in Middle English and Early Modern English) was the default ending for verbs conjugated in the third person present simple form. In accordance with this belief, "my cup runneth over" is simply an old way of saying "my cup runs over".
I hope this was helpful. đ