To make something larger fit in a smaller or tight place with brute force
To insert an extra month into a calendar for the same purpose. The Hebrew calendar has such a month.
To insert a substance between two or more molecules, bases, cells, or tissues.
To insert an extra leap day into a calendar in order to maintain synchrony with natural phenomena.
To insert anything somewhere (especially between other things), such as an affix into a word. (Compare interpolate.)