A conclusion paragraph should begin by reiterating the paper's main claim. In other words, the last paragraph should echo the thesis statement laid out in the introduction. In order to avoid dull repetition, however, different wording should be used when recapping the paper's position. For example, if your thesis statement reads, "Many Californians are buying the Brand X car because of its excellent fuel economy and high resale value," then an acceptable summary of the claim in the conclusion would read as follows: "Excellent fuel economy and high resale value have contributed to the popularity of the Brand X in California."
Supporting arguments lend authority and validity to claims made in the thesis. Because of this, summarize your main arguments in the conclusion after you have restated your thesis. Doing so will lead to a well-integrated and focused conclusion, one that will leave little doubt as to the paper's position on the subject matter.
Try to answer the question "So what?" in your conclusion. Doing this will give your readers a clear understanding as to why your paper is important. Challenging readers to consider the broader implications of a topic may intrigue them to think beyond the scope of your paper and consider new points of view on certain issues.
Avoid introducing new ideas, arguments or details to an essay in the conclusion. The purpose of the conclusion paragraph is to provide closure for the paper, not to propose new details. In addition, avoid shedding doubt on your claims by introducing counterintuitive thoughts or by using meaningless cliches.