1. "Dem Feels" means "them (those) feelings"... often used in the context of something that involves a large amount of emotional involvement or response, such as a particularly dramatic television show, movie, book, or real-life event; and the sharing or accepting of those emotions.
2. A meme relating to the above
(guy 1) "My girlfriend was killed by a drunk driver... I feel so alone."
(guy 2) "ok bro, Gimme all dem feels"