Paragraphs are a relatively new invention (17th century). Printers started using paragraph divisions to give the reader's eyes a break. Paragraphs give the reader's mind a break, as well. I like to think of them this way: an essay is all about one topic; its paragraphs are about subtopics of that main topic. Each time the (sub) topic shifts, it is time to start a new paragraph. This helps to rest the readers' eyes and guide their minds.
Here, I am shifting the topic from the background of paragraphs to the various ways people actually use them, so I have started a new paragraph. Newspaper writers often use very short paragraphs, partly because the text is presented in narrow columns, and the paragraph divisions break the columns up into chunks. Wider columns, of course, could use longer paragraphs and get the same visual effect. However, perhaps unfortunately, news is also presented in short bits. On TV, we call them "sound bits." Let's call the written version, "eye bits." These eye bits are the paragraphs that you see in a newspaper.
In a college essay, readers expect somewhat meatier chunks than the very short paragraphs of a newspaper article. Here is a good rule of thumb for writing essays: if you find yourself writing very long paragraphs, ask if the topic is shifting, and if the answer is yes, start a new paragraph. On the other hand, if you find that you are writing a series of very short paragraphs, ask yourself if you can develop your ideas in more detail--that is the key to making more substantial paragraphs.
