For those who don't know much about the show this is the premise from Wikipedia:
[edit] Story
In the pilot episode, we see approximately twenty years into the future where an aging Batman equipped with a high-tech Batsuit takes on the kidnappers of Bunny Vreeland. During the battle, Batman suffers a heart attack which forces him to betray a lifelong principle by threatening a criminal with a gun. Because of this, Bruce Wayne reluctantly decides to retire the Batman persona.
The story then fast-forwards another twenty years. Gotham City is now a futuristic megalopolis equipped with staggering high rises and hovering/flying vehicles. Bruce Wayne is now a recluse, living in bitter isolation with no companion but his guard dog, Ace. It is implied by virtue of his continuing to fight crime long after he should have, and his retaining of the costumes worn by Robin, Nightwing, and Batgirl, that even before he had a heart attack, something horrible transpired that caused Bruce to sever his ties with the Justice League and forbid his disciples to ever again assume their alter-egos. The events which caused all of this are revealed in Batman Beyond: Return of the Joker.
In 2039, Terry McGinnis (born on June 27, 2023) is an athletic sixteen year-old high school student and reformed troublemaker with a deeply ingrained sense of personal justice. During the pilot episode, he saves a fellow passenger on a commuter rail from a member of the Jokerz gang, and later single-handedly takes on an entire gang of them to defend his girlfriend, ultimately resulting in a harrowing high-speed motorcycle chase through Neo-Gotham's expressways. The chase ends at the doorstep of Wayne Manor, where a fleeing Terry runs into the elderly Bruce Wayne. Bruce and Terry fend off the Jokerz side-by-side, but the exertion aggravates Wayne's heart condition. Terry helps Bruce back to the manor, and while staying there, he discovers the entrance to the Batcave. He later returns to "borrow" the Batsuit to avenge the death of his father. As crime and corruption are beginning once again to rear their ugly heads in Gotham, Bruce ultimately allows Terry to assume the mantle of Batman.
Terry continues the battle against crime, tutored by Bruce and aided by a new, high-tech Batsuit that augments his abilities, fires Batarangs from the wrists, flies using jets fired from the feet, allows eavesdropping through a hypersensitive touch microphone, and provides camouflage abilities. He comes to have his own rogues gallery, such as the seductive shape-shifter Inque, the hypnotist Spellbinder, the bitter, deaf sound expert Shriek, the deadly assassin Curare, the insane terrorist Mad Stan, the African hunter Stalker, a new version of the Royal Flush Gang, and the Jokerz, a gang idolizing the notorious Joker. However, on occasion, Terry is also forced to face his mentor's old foes, such as the atrophying Mr. Freeze, Bane (elderly, wasted, and dying from his consumption of Venom, the substance that gave him his strength), the immortal Ra's al Ghul, and even a reborn Joker.