Something indivisible cannot be broken up or divided: it's rock solid.
The most common use of the word indivisible is in the Pledge of Allegiance, where it is used to show how our country is united and can't be broken up. But you can use this word for any group or organization that seems indestructible. Anything that can be broken up, separated, or smashed into pieces is divisible, not indivisible. In math, you can say that the number 9 is indivisible by 2: it can't be divided by 2 evenly.