The original Digimon Tamagotchi toys weren’t super cannon to the lore that got built up in the animes. They were more akin to the Pocket Pikachu in that you were just raising a lil guy.

In the shows, the digital world is a consequence of technology. Kinda. It’s accessible via computers and stuff. It is, like, “housed” on the internet, but it’s a fully parallel universes (basically). This can change a bit per series (or maybe I’m misremembering).

Digimon live there naturally and have their own wants and dreams. Some are more animalistic in nature and intelligence, but most are sapient and can speak. Some Digimon are a direct result of humanity’s thoughts and feelings and are based on real world myths. Others seem to be wholly unique creatures.

In “the wild” Digimon can Digivolve naturally based on their age. This type of Digivolution is seemingly permanent. If the Digimon is paired with a human partner, and there is a Digivice involved, they can attain higher levels without needing to age up, and they can return to their previous state after a time.

The Digivolution track is not linear. What branch they go down depends on a few factors, but is mainly an emotional thing. An angry Digimon will Digivolve into a different form than the same type of Digimon that is happy. In Digimon Adventure 01 for example, Greymon will normally Digivolve into MetalGreymon. One episode he is forced to Digivolve by his partner though, and becomes a much more evil SkullGreymon. When Digimon Digivolve they mostly maintain their memories, but the new forms can sometimes come with drastic personality changes. Kinda like how Ash’s Charizard was obstinate compared to the much more agreeable Charmander it started out as.