The Lego Batman Movie is a spin-off of 2014's The Lego Movie, starring (Lego) Batman, one of that film's most memorable side characters. It also serves as something of an affectionate parody to the Batman franchise, particularly its more "dark and gritty" adaptations, resulting in a fun yet surprisingly poignant examination of the classic character.
Batman (Will Arnett) works alone. Pretty much literally—the Gotham Police don't really know what to do other than turning on the Bat-Signal, while his loyal butler Alfred (Ralph Fiennes) runs Batman's personal life. This changes when Barbara Gordon (Rosario Dawson) takes over as commissioner; she wants the police to have a more active role working alongside Batman, but he's not willing to share the spotlight. Meanwhile, he accidentally adopts a boy named Dick Grayson (Michael Cera), all while the Joker (Zach Galifianakis) tries to recruit an army of villains to take over the city.
If you're a fan of this superhero, you'll find lots of little Easter eggs, including plenty of sillier, Silver Age villains ("Might be worth a Google!") Even some aspects, like Barbara "Batgirl" Gordon being an adult several years older than Dick "Robin" Grayson, hearken back to the characters' earlier, now retconned comic roots. Much of this ties into the parody aspect of the film: there are some slight digs at the different incarnations of Batman's character, including even last year's entries into the DC Extended Universe.
Batman himself is naturally exaggerated and changed a bit; a rather vain glory hound, he's familiar to fans of The Lego Movie but quite different from the comics. It seems odd, given how much he dislikes the people around him, but this makes a surprising amount of sense; he needs the cheer of the crowd precisely because he won't let anyone close to him, even keeping Alfred more distant than in many adaptations. Naturally this changes over the course of the film, as the cheerful enthusiasm of Dick, steady loyalty of Alfred and tough-but-fair friendship of Barbara brightens his dark heart. (And don't worry, people who hated The Killing Joke—it looks like she'll be a love interest, but she's actually just a "platonic work-colleague, who's a girl.")
Unlike Batman, the Joker is a team player from the start, even if he's willing to betray his team when it's convenient. Obviously he's not the murderous icon of madness that he is in most incarnations, but still manages to be quite funny, his hatred of Batman coming off like a needy girl trying to get her aloof boyfriend to commit. He does seem to be dating Harley Quinn (Jenny Slate), though, and thankfully their relationship is actually healthy.
All in all, The Lego Batman Movie is, like its predecessor in the Lego Cinematic/Extended Universe, both funny and heartfelt, and a nice antidote to those who want some childish wonder back in their dark superhero films. And remember: Friends Are Family!