What does incognito mode do?
Put simply, using a private browsing window prevents Chrome (or whatever browser you're into these days) from storing information like URLs, cached page text, and records of the files you download. Put even simpler, it's ideal for visiting pages and conducting web searches that you don't want ending up in your autocomplete settings or browser history. So whether you're doing some surreptitious Christmas shopping or late-night porn browsing, you'll wanna switch over to your browser's incognito-mode equivalent.
There's actually another handy use for private browsing that's got nothing to do with hiding your activity: If someone needs to sign into a site you're already logged into (Gmail, Facebook, Amazon, etc.) on your computer, just have them open an incognito window. It'll let them sign in without kicking you off, and it's easier than opening a totally different browser -- even better, they don't even have to worry about signing out since their session is terminated as soon as the incognito window's closed.