Paragraphs are the building blocks of an essay, so the difference between the two is comparative to the difference between a brick and a house. Your house may be made of bricks, but it's not likely you'll ever live in just a single brick.
Both a good paragraph and a good essay make a point. One thought logically flows into another with one central point in mind.
A paragraph includes a topic sentence that is followed by at least two to three sentences that elaborate on that topic. It ends with a final sentence that sums up those thoughts and reaches a conclusion about them.
An essay includes an introduction that presents a topic followed by at least two to three paragraphs that elaborate on that topic along with a final paragraph that sums up those thoughts and reaches a conclusion about them.
The difference is that the topic in an essay is generally broader and requires multiple paragraphs to explain the points its writer intends to make about that topic.
A good paragraph makes a point and each sentence supports and expands on that one point. Paragraphs should be limited to a single topic and each body sentence should simply flesh out the topic at hand. Traditionally, a paragraph should include at least four to five sentences of writing with this specific structure in mind to be complete.
A good essay includes a thesis statement that can be expanded to make many points that relate back to it. Each paragraph in an essay will include a topic sentence that both support and flesh out the thesis statement. Further, a good essay takes quite a bit more preparation than a single paragraph. Few good essays include less than five paragraphs since a much broader topic is being explored than in a single paragraph.
The ability to write a good paragraph is essential to writing a good essay. However, you're going to have to work a little harder on an essay, because a single paragraph is generally not going to make a broad enough point to be considered an essay. Use good, well-structured paragraphs with topic sentences that make each point in explain a thesis statement as your building blocks, and you'll be well on your way to completing a great essay.