Persistent cookies help websites remember your information and settings when you visit them in the future. This results in faster and more convenient access since, for example, you don't have to login again.
Besides authentication, other website features made possible by persistent cookies include language selection, theme selection, menu preferences, internal site bookmarks or favorites, among many others. On your first visit, the website is presented in default mode. During your visit, you select your preferences and these preferences are remembered, through the use of the persistent cookie, the next time you visit the site.
For example, a website may offer its contents in different languages. On your first visit, you may choose to have the content delivered in French and the site may record that preference in a persistent cookie set on your browser. When you revisit that site it will use the cookie to ensure that the content is delivered in French.