A paragraph focuses on one topic. This topic is introduced with the first sentence in the paragraph, and the following sentences provide supporting details about the topic. An essay is usually composed of multiple paragraphs and can focus on a much larger topic than an individual paragraph can. It will typically be structured similarly, though. For example, in a five-paragraph essay, the first paragraph introduces the broad topic of the essay. The next three body paragraphs all focus on individual, smaller topics within the broad topic. The final paragraph concludes the essay by summarizing the main arguments.
Yes, technically speaking this sentence is properly punctuated, although it should be noted that this is somewhat a matter of style, since there could be a period where the semi-colon is.
