Nexus Premium is a paid subscription that grants certain perks to users, including removal of all ads and faster downloads. The Nexus has also added an additional click to the process of downloading a file which includes a countdown and an ad for the Premium membership to further incentivise purchasing a subscription.
I recommend holding off on Premium until you have progressed enough in your modding journey to know that you will stick with it for a while. When building a larger mod setup, paying for a month or so of Premium can be well worth the asking price. It is also a great way of giving back to the Nexus for their service, especially for those of us with ad blockers installed.