Disunity is a state of disagreement and conflict in a group of people. If you and your siblings are bickering loudly about who gets to sit in the front seat of the car, that's a good example of disunity.
When people experience disunity, they just can't get along — in other words, they're not united. Unity, "the state of being one," comes from the Latin unitatem, "oneness, sameness, or agreement." Adding the prefix dis-, "not, or lack of," gives you the exact opposite. The disunity of a country can be seen in bitter political rhetoric, and your book group shows disunity when the members argue incessantly over what to read next.