Something has divisibility if you can split it into different sections or portions. If you've learned basic rules of divisibility in math class, you know that all even numbers can be evenly divided by 2.
In math, divisibility refers to a number's quality of being evenly divided by another number, without a remainder left over. You can easily see the divisibility of 40 by 4, for example. The divisibility of a large piece of land means that it can be broken into smaller parcels to be sold separately, and the divisibility of a pan of brownies is clear when you slice into it and dole out equal portions to all of your friends.