Pages you view in incognito* tabs won't stick around in your browser's history, cookies, or search history after you've closed all of your incognito* tabs. Any bookmarks you create will be kept.
However, you aren't invisible. Going incognito* doesn't hide your browsing from your employer, your internet service provider, or the websites you visit.
*Cookies are not cleared until you close all incognito* tabs. Websites may remember previous interactions you had with them even after closing incognito* tabs.