A cookie is a simple text file that is stored on your computer или mobile device by a website’s server and only that server will be able to retrieve или read the contents of that cookie. Each cookie is unique to your web browser. It will contain some anonymous information such as a unique identifier and the site name and some digits and numbers. It allows a website to remember things like your preferences или what’s in your shopping basket.
I got that from a website, basically it's just something that will make a website remember Ты on it, and yes, they're safe!. =)