This line derives from Psalm 23:5 in the Bible:
You prepare a table before me
in the presence of my enemies.
You anoint my head with oil;
my cup overflows.
The overflowing cup is a metaphor for God filling a person with joy, contentment and everything that they could need, so much so that it seems to be spilling out of them. The phrase, more often quoted as ‘my cup runneth over,’ has since been used to indicate that a person is bursting with happiness and satisfaction, or that they have more than enough of what they need or desire.