For the dinosaurs in the audience, The typical use of this meme is when you'll be watching some sort of "you laugh you lose" or really any sort of commentary video/livestream where they might insert a funny gif or have a visual gag with some romantic or sexual edge to it, such as the one attached below.
Upon seeing this somebody will usually comment "hear me out" as if they are offering a defense as to why it's reasonable that they are sexually attracted to this character as part of an imaginary conversation that the reader would be having with them, where the reader is chastising them for having such thoughts. It's not that funny. It's just one of the many types of phrases that gets squawked by the "chat" in these videos.
