Your conclusion is your opportunity to wrap up your essay in a tidy package and bring it home for your reader. It is a good idea to recapitulate what you said in your Thesis Statement in order to suggest to your reader that you have accomplished what you set out to accomplish. It is also important to judge for yourself that you have, in fact, done so. If you find that your thesis statement now sounds hollow or irrelevant — that you haven't done what you set out to do — then you need either to revise your argument or to redefine your thesis statement. Don't worry about that; it happens to writers all the time. They have argued themselves into a position that they might not have thought of when they began their writing. Writing, just as much as reading, is a process of self discovery. Do not, in any case, simply restate your thesis statement in your final paragraph, as that would be redundant. Having read your essay, we should understand this main thought with fresh and deeper understanding, and your conclusion wants to reflect what we have learned.
There are some cautions we want to keep in mind as we fashion our final utterance. First, we don't want to finish with a sentimental flourish that shows we're trying to do too much. It's probably enough that our essay on recycling will slow the growth of the landfill in Hartford's North Meadows. We don't need to claim that recycling our soda bottles is going to save the world for our children's children. (That may be true, in fact, but it's better to claim too little than too much; otherwise, our readers are going to be left with that feeling of "Who's he/she kidding?") The conclusion should contain a definite, positive statement or call to action, but that statement needs to be based on what we have provided in the essay.
Second, the conclusion is no place to bring up new ideas. If a brilliant idea tries to sneak into our final paragraph, we must pluck it out and let it have its own paragraph earlier in the essay. If it doesn't fit the structure or argument of the essay, we will leave it out altogether and let it have its own essay later on. The last thing we want in our conclusion is an excuse for our readers' minds wandering off into some new field. Allowing a peer editor or friend to reread our essay before we hand it in is one way to check this impulse before it ruins our good intentions and hard work.
Never apologize for or otherwise undercut the argument you've made or leave your readers with the sense that "this is just little ol' me talking." Leave your readers with the sense that they've been in the company of someone who knows what he or she is doing. Also, if you promised in the introduction that you were going to cover four points and you covered only two (because you couldn't find enough information or you took too long with the first two or you got tired), don't try to cram those last two points into your final paragraph. The "rush job" will be all too apparent. Instead, revise your introduction or take the time to do justice to these other points.
Here is a brief list of things that you might accomplish in your concluding paragraph(s).* There are certainly other things that you can do, and you certainly don't want to do all these things. They're only suggestions:
Here is the concluding paragraph of George Orwell's famous essay, "Politics and the English Language." If you would like to read the entire essay from which this conclusion is taken (and check out, especially, the beginning), click HERE.
I have not here been considering the literary use of language, but merely language as an instrument for expressing and not for concealing or preventing thought. Stuart Chase and others have come near to claiming that all abstract words are meaningless, and have used this as a pretext for advocating a kind of political quietism. Since you don't know what Fascism is, how can you struggle against Fascism? One need not swallow such absurdities as this, but one ought to recognize that the present political chaos is connected with the decay of language, and that one can probably bring about some improvement by starting at the verbal end. If you simplify your English, you are freed from the worst follies of orthodoxy. You cannot speak any of the necessary dialects, and when you make a stupid remark its stupidity will be obvious, even to yourself. Political language — and with variations this is true of all political parties, from Conservatives to Anarchists — is designed to make lies sound truthful and murder respectable, and to give an appearance of solidity to pure wind. One cannot change this all in a moment, but one can at least change one's own habits, and from time to time one can even, if one jeers loudly enough, send some worn-out and useless phrase — some jackboot, Achilles' heel, hotbed, melting pot, acid test, veritable inferno, or other lump of verbal refuse — into the dustbin, where it belongs.
*The list of things that you might do in a concluding paragraph is taken from the University of Richmond's online document, Writing Conclusions (with the gracious permission of UR's Writer's Web coordinator, Joe Essid).