Free beats are usually a way for producers to showcase their talent and expose their work to more people who may have not have heard of them. It’s a promotional tactic in which both producers and artist benefit. Now they aren’t free in the sense that they are yours and you own them, but you usually will have a free license to use them.
Free downloads (also known as Demo Downloads) are similar and in most cases they are strictly for demonstration purposes only. Producers usually make these available to artist who may want to record their vocals over the beat to preview before making a final decision on whether they wanted to buy it. Some producers allow you to use their demo downloads for non-profit use, but most producers require you to purchase a license before you release your song to the public.
They usually come with a basic license agreement. If your not familiar with what beat licenses are, I wrote a blog post about it here.
These are for artist who may be just starting their career or who may not have the money to purchase a license at the time. We all have lives and can use a break every now and then, that’s when free instrumentals can really be useful.