Proofreading is the last step in your writing and editing process. You should have written and edited your work for general coherence and flow before proofreading. In the publishing world, there will be several stages of editing before reaching the proofreading stage (including substantive editing and copy or line editing); however, when you are revising your own work, you'll probably combine line editing (a grammar and spelling check) with proofreading (checking for typos, formatting and style).
Proofreading symbols make this process relatively painless and are designed to save you time while improving the quality of your work. You can use these symbols to correct misspellings, punctuation errors, and even formatting issues. Below are the most commonly used symbols; you can find more on the Chicago Manual of Style's website.