Unity simply means that all sentences support the topic and the controlling idea.  Supporting sentences must support the topic sentence using examples, details, definitions, or steps.  Then the concluding sentence restates the topic sentence.

Let’s take a moment and look at an example.  Notice in this example that one sentence does not support the topic sentence.

With the widespread use of the cell phone, many teenagers have become addicted to texting. The average teenager texts 2,000 to 3,000 messages every month. Companies are developing new ways to communicate globally. This addiction has caused alarm, as teenagers prefer to communicate even in the same room by texting. Experts suggest that parents should limit cell phone use to help teenagers overcome their addictions.

As we read the paragraph, did you notice the sentence that breaks unity?

Let’s look at the paragraph again. The Topic Sentence says, “…many teenagers have become addicted to texting.” Which sentence in the paragraph does not support the topic?
Notice the sentence in the middle of the paragraph. “Companies are developing new ways to communicate globally.”  This sentence is about companies developing new ways to communicate globally. It is not about teenagers becoming addicted to texting.  This sentence breaks the unity of the paragraph.