Digimon were originally part of the cute, but amazingly annoying Tamagotchi pets produced by Bandai around late-1995. The success of the virtual pets inspired the company to create a similar product targeted at boys, and so it was in June of 1997 that Digimon were unleashed, similar to the Tamagotchis in that one had to care and maintain them, but the difference was that kids could now hook up their Digimon and proceed to battle each other as well as allowing their Digimon to grow more powerful and stronger (i.e. Digivolving). Digimon's success was fueled by another growing craze in Japan...Pokémon which at that point had already spun-off its own TV show.
Seeing the success of Pokémon and a growing interest in its own Digmon products, Bandai decided to create a card came as well as an animated series for Digimon. Hiring Toei Animation, one of Japan's largest animation studios, the Digimon animated series, "Digimon: Digital Monsters," hit Japanese TV in 1998 and soon after negotiated with Saban Entertainment (Ugh!) and Fox Kids to bring the series to the United States. The show premired in Agust of 1999 with enormous success spawning Playstation games and even a box office movie, Digimon: The Movie (This was 3 movies in Japan).
Today, Digimon is a international sucess. The TV show, now awaiting its 4th season is broadcasted in Europe, South America, Canada, and many parts of Asia.
Oh, and I suppose I should comment on the "Which came first, Digmon or Pokémon," question. I would say...depends. If you counted Tamogatchi and the fact that the idea was already ready and set before the Pokémon craze, yes. Otherwise, it was Pokémon by a few months. Although quite frankly...I'm not sure how they're directly related.