Click the icon to toggle the cookieBehavior preference, that's all it does.
When it enables cookies, it intentionally still disallows all third party cookies unless you right-click the icon to toggle the thirdparty.sessionOnly preference (the cookie icon puts on a party hat and the status shows in a tooltip when hovering over the icon). Then it'll only allow third party cookies from sites you've already visited and won't retain them upon the next restart of Firefox.
This is primarily for people who like to keep cookies disabled unless it breaks a site, never want permanent third party cookies, and probably have the "Ask me every time" option selected to control exceptions like a whitelist (tip: that option is more bearable when you set the about:config pref network.cookie.alwaysAcceptSessionCookies to true for less repetitive prompting)
Bonus: Middle-click the icon to open your cookies list in a new tab.
Extra Bonus: Hold down Shift or Ctrl when middle-clicking the icon to open about:config?filter=network.cookie in a new tab for anyone curious to view pref changes live as you click/right-click the icon.