The original show ran for two seasons and 30 episodes from April 1990 to June 1991. It opened with the murder of Laura Palmer, a young girl in the town of Twin Peaks, and FBI Agent Dale Cooper is called in to help investigate the crime. However, what initially appears to be a mundane if horrific crime rapidly expands to incorporate bizarre spirits and an other-dimensional location known as the Black Lodge. Cooper helps solve the crime - and other related cases in the town - by interpreting his dreams and communing with the spirit of Laura Palmer.
The first season was a titanic critical and commercial success, with massive ratings and critical acclaim, as well as appreciation for its tightly-serialised storytelling (highly unusual in 1990, when most shows were episodic with no long-running storylines). The second season, mostly helmed by other writers as Lynch and Frost took a back seat, was considerably less well-received, especially after the resolution of the Laura Palmer murder mystery halfway through the season and relatively few answers being given to the show's many questions. However, the ending to the season was better-received, especially the revelation that the Palmer murder was setting in motion a much bigger and darker storyline. Sadly, this was not enough to save the series from cancellation.
The series was, arguably, the first harbinger of today's big watercooler shows, and its mix of critical and commercial acclaim gradually giving way to disappointment would later be replicated in both The X-Files (which inherited David Duchovny, one of Twin Peaks' recurring castmembers and who is returning for the new show) and Lost. David Lynch himself frequently expressed dissatisfaction with the ending of the series and resurrected the franchise in 1992 for a prequel movie, Fire Walk With Me, which fills in Laura Palmer's backstory and hints at Agent Cooper's fate after the show's cliffhanger ending, as well as having David Bowie show up for no discernible reason. The movie was slated and bombed at the box office, but has seen a positive critical reassessment in more recent years.
Many of the surviving castmembers from the original series return, most crucially Kyle MacLachlan as Dale Cooper. The 25-year gap since the original series will be acknowledged and will play a key plot point (helped by the ghost of Laura Palmer saying "See you in 25 years" in the final episode), and the Fire Walk With Me prequel movie will be considered canonical. Presumably the series will explain what happened to Cooper after the cliffhanger ending to the show's final episode, which appeared to show Cooper possessed by the murderous entity "Bob".
Twin Peaks has been a huge influence on everything from the aforementioned X-Files and Lost to more recent fare like Stranger Things and the Alan Wake video games.
Showtime have described the show as "the pure heroin version of David Lynch", which is both intriguing and terrifying. Whether the new Twin Peaks can resurrect the same kind of power as the original show remains to be seen, but we'll find out in May when it airs in the US and on Sky in the UK.