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, depending on the producer, you usually can use them for free for non profit use (Not making money in any way).
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.