A cookie is a harmless text file that is stored into your browser when you visit almost any website. Their usefulness resides in allowing the website to remember your previous visits. Despite most people not knowing, they’ve been in use for 20 years, when the first browsers appeared.
They’re not viruses, trojans, worms, spam, spyware or open pop-up windows.
The cookies don’t usually store sensible information about you, like credit card or bank information, photos, identity numbers or other personal information. More commonly, they store technical data or personal use preferences.
The web server doesn’t associate the cookie to yourself as a person, but to your web browser instead. If you usually browse with Internet Explorer, you’ll notice if you try Firefox that the websites don’t seem to recognize you.
The propietary cookies are the ones generated by the website you are visiting, and the third-party ones are generated by external services, like Facebook, Google, Twitter, etc.
Yes, and not only delete, but also block them further, in general, or for a web domain in particular.
To delete the cookies, go to the settings options of your web browser and there search for the cookies options and the ones associated to the domain you want to delete them for.