Great (and correct) answers already, but I wanted to add a shorter version.
Not only are you consenting to storing information in your browser, but also to *send* it to whoever they want; You are allowing the site to configure your browser to automatically send data describing your actions and history to them and other parties.
The only difference now is that they have to get your consent before doing it. Before they did it without asking or letting you know. An arguably unfortunate side-effect of this is that it has lead to people consenting just to make the internet work, so the site owners can insert whatever else there for people to agree to without reading it.
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