Batman: The Animated Series aired between 1992 and 1995, producing 85 episodes and spawning a number of spin-off shows and series set in the same continuity. The series is one of the most highly-acclaimed animated and superhero TV series of all time and has recently reached new audiences through a HD remaster and appearing on streaming services.
The show drew on Tim Burton's live-action movies Batman (1989) and Batman Returns (1992) for artistic inspiration, although it also charted its own course with unique characterisations for Bruce Wayne/Batman, Robin and Joker. The vocal performances by Kevin Conroy (Batman), Mark Hamill (Joker) and Arleen Sorkin (Harley Quinn) have also become regarded as iconic, if not definitive. The show is also highly notable for its additions to the Batman mythos, most infamously the character of Harley Quinn who was introduced in the animated series before migrating to the comic a year later. Renee Montoya, Lock-Up and Simon Trent are other characters originated on the series to play a role in other versions of the mythos later on.
The Animated Series version of the mythos directly inspired the storylines and characterisation in the Arkham series of video games, which also starred Conroy, Hamill and (in the first game, at least) Sorkin.
Smith indicates that Bruce Timm, the original showrunner and co-creator, is involved in the new series. It's unclear if writer Paul Dini is also on board, or if the original vocal cast will return; Hamill, at least, has said that his version of Joker has been retired (although he's also been tempted out of retirement in the past).
If the continuation is confirmed, it is unclear if it would be a reboot in the same art style or if it would continue the storylines from where the animated show left off. This might be complicated by the sheer number of other series which have followed on from The Animated Series (including a contemporary Superman series and the SF-tinged Batman Beyond).
HBO Max has not yet formally confirmed the news.