Look at the web address, does it show "http" or "https" in the address line? Addresses starting with "https" should be secure. For various reasons a connection might be established through "http" without the added security, so that is what the warning refers to.
Various cookies get loaded as you visit various sites on the web. Some capture data to serve you with local adverts or monitor your browsing behaviour. These cookies can remain active until you close the browser even though you have left the site.
Open a new browser session and window for sites that you know you want security to be active such as on line banking. Close down the browser and restart on e you have completed your transaction.
Chrome can be a bit sensitive about the possibility of security risks too, but better safe than sorry.