This is a tiny, non-commercial website based out of the USA, so it is not subject to the GDPR of Europe or it's required notifications about tracking cookies. However, because the regulation isn't without merit, I'm taking it on myself to tell you that when you visit my website, you will receive a cookie.
Software uses variables in order to do what it does. Variables are data that can change each time the software runs, such as the current date, the identity of the user, or what input the user submits. When the software runs on your computer, such as a word processor or your operating system, naturally all the variables the software uses are stored on your computer alongside the software.
However, when the software is a website (such as the one creating the page you are reading right now) that data can be stored either on the server running the website, or on the computer loading the website – e.g. your computer.
When that variable is stored on your computer, it is called a "cookie." The cookie is very small: it is a variable name and then the variable value, usually just a few characters long. While any number of cookies could bet set on your computer by the website, typically only one cookie is needed: an identifier. By setting an identifier cookie, then each time a page is loaded, the website knows that it is you loading that page and nobody else. Cookies allow modern web apps to exist – they are what allow you to create accounts, login to websites, and post things online. Without cookies, the web as we know it is not possible.
The problem, of course, is when those identifier cookies are used to track you. You presumably want to be tracked when you are, for instance, logged into your email. When you load your email, you want to see your email and not someone else's. There is benefit to being 'tracked' in this situation. However, you do not necessarily want to be tracked when you are not logged in. Tracking you when are not logged in can be benign, such as a website wanting to know which of the links on their homepage generate the most interest. But tracking can and does quickly escalate into gathering far more information than necessary.
As we have famously seen, detailed tracking our every interaction allows companies and governments to build profiles on us. In an extreme-sounding yet depressingly realistic example, tracking is combined from multiple, disparate websites to create dossiers on what we read, what we buy, what we watch, who we interact with, what we say, and (presumably) how we feel. The data grows specific enough that it can be de-anonymized and tied back to our identities. The net effect is that through website tracking we live in a state of constant surveillance, a panopticon of emergent design.
Unfortunately, cookies are not the only way to track users on the web. Cookies were the first way, but since then, software engineers have come up with myriad ways to de-anonymize visitors to their websites, putting identity to everyone who uses their service, whether logged in or not. There exist techniques to minimize this tracking, and privacy tools to help fight back, but there is no easy solution to being both a user of the modern web and not being tracked – we cannot have our cake and eat it too.
Yes, when you visit the brandensite, the brandensite will set a cookie on your computer. It is called "htscallerid" and the value will be unique to your session. This cookie is technically a tracking cookie. You are "tracked" so that the interactivity of this website will work. However, no data is collected about you. This website does not log anything about you other than your existence because I don't want it to. I have no need for the data, nor any desire to contribute to the surveillance state. And even if it did log your data (which it doesn't) I have no partners or 3rd party services with which that data (which doesn't exist) could be shared.
So, yes, the brandensite uses a cookie. But, no, it's not a big deal.