The topic sentence communicates the main idea of the paragraph. If the topic of the paper is mushrooms, for example, the topic sentence for one paragraph will state a fact about mushrooms. The rest of the paragraph is coherent when it continues the idea of the topic sentence and discusses the mushroom fact.
The main points of the paragraph clearly support the topic sentence. Each sentence will be tied to the topic sentence in some manner. Adequate development happens when each of the main points within the paragraph relate to the topic sentence. Following the previous example, a paragraph on mushroom habitats will talk about caves as one main point and forests as another point, rather than discussing that mushrooms are fungi.
The conclusion of the paragraph wraps up the ideas and leads the reader into the next paragraph. This seems like a good deal of work to ask from one sentence, but experience teaches writers how to complete this task well. Following the previous example, a sentence that works as a conclusion would be, "Mushrooms grow in deciduous forests but will cause tree rot when protruding from a live tree." The next paragraph will discuss problems caused by mushrooms.
Unity within a paragraph ties the topic sentence, main ideas and conclusion into one. The paragraph needs to focus on one single idea. Other ideas are best saved for other paragraphs within the same paper. Read paragraphs again to ensure unity; if necessary, separate the paper by paragraph and read each one separately to search for unity.