Digimon: Digital Monsters is a TV show, toy line, virtual pet, and trading card game.  The first Digimon released was a virtual pet.  People could train and then battle their Digimon.  Digimon has always been considered a copy.  Originally, people called it a copy of Tamagotchi's and when the TV show came, people called it a copy of Pokemon.  Neither of these statements is entirely true because Digimon was the first battling virtual pet and the virtual pets were actually out before Pokemon.

Digimon is focused around monsters that come from the digital world.  These creatures can become stronger and when they get strong enough, they can digivolve to their next level.  The levels are: digiegg, baby, in-training, rookie, champion, ultimate, and mega.  An example of this is Digiegg, Punimon, Tsunomon, Gabumon, Garurumon, Weregarurumon, Metalgarurumon.  babies have no attacks, in-training Digimon all know bubble blow, and from then Digimon have unique attacks, although some Digimon share the same attack.  For instance, all digimon know defend, and both Megakabuterimon and Tuskmon know Horn Buster.
All Digimon have names that end in "mon", and when some Digimon evolve, they simply get a prefix added to their name, like when Greymon digivolves to Metalgreymon.

There has been one english Digimon movie and two more are to follow.  The first movie shows how the eight kids were chosen to be the Digidestined, the second happens a year after the kids defeat Piedmon and return home.  The third happens a year after season two.  Some of the original Digidestined return to help.  Season two happens three years after the digidestined defeat Piedmon.  Several new kids, along with T.K. and Kari, becokme the new digidestined team.  In season two Patamon and Salamon both return as well.  All of the good Digimon now can digivolve into two different champions.