to increase in quantity: to become many or much, or to make something become many or much.
At heart this word is about a quantity going up. Something that was few or small in amount ends up many or large. It is used of people, of a harvest, of a message travelling, and even of wrongdoing. The closest English words are "multiply" and "increase," and both serve well, although English "multiply" carries a hint of arithmetic that the Greek never has.
The word faces two directions. Said of a group or a thing on its own, it reports that the group or thing got bigger: the Israelites in Egypt, the disciples in Jerusalem, the churches spread across Judea and Galilee and Samaria. Said of someone acting on something, it reports that this person made it bigger, and in the New Testament that someone is always God, who enlarges the family promised to Abraham and the harvest of a generous giver.
Those are not two words but one increase seen from either end, and the New Testament writers keep both ends in view at once. Luke almost never names who is doing the multiplying, and that silence is the point: the growth of the early church is reported as something happening to it rather than something it managed.
One set of uses rounds the word off. Three letters open with a wish that grace, peace, mercy, and love would be "multiplied" to the readers. That is a formal greeting inherited from the royal Aramaic letters in Daniel, where a court scribe wishes that the reader's peace would increase (שְׂגָא), and it asks not for a larger number of anything but for these gifts in ever fuller measure.