to overflow: to be present beyond the measure that is needed, so that there is a surplus, growth, or plenty
The picture behind this word is going past a limit. Whatever it describes is not merely adequate; there is extra. It is the food that was left over after the crowds had eaten their fill, the rich giving out of what they had to spare, the person who has more than enough on hand.
Paul takes this everyday picture of surplus and makes it one of his favorite ways to describe God's generosity and the shape of the Christian life. Grace, comfort, joy, love, hope, and thanksgiving all overflow. Believers are urged to overflow more and more in love and in good work. It is a word of abundance and increase, never of bare sufficiency.
The verb points in two directions. Usually something simply overflows on its own: grace abounds, sufferings abound, a ministry overflows in thanksgiving. But it can also say that someone makes something overflow. God is able to make grace overflow toward his people, and to make them increase and abound in love. The same word covers both the overflowing and the causing of it.