Story Mode is how Digimon Alysion introduces its systems, and it does so by using the Digimon Liberator webcomic and light novel as its setting. Both are free to read on the official Digimon Card Game site, so the story context is available at no cost whether you are playing the digital game or not.
The protagonist is Kanata Hondo, voiced by Shu Uchida. She is an energetic, upbeat newcomer to card games - the tutorial character, essentially, and the entry point for players who have never touched a TCG. The Story Mode frames learning the Digimon Card Game as something Kanata goes through, so the tutorial content arrives as story rather than as an interruption.
Kanata's best friend Futre, voiced by Hikari Kubota, is an online gaming friend she has never met in person. Their dynamic - one enthusiastic newcomer, one more experienced player - is the tutorial structure of the story mode in narrative form.
The voice cast includes Fairouz Ai as Valner Dragnogh, guild master of [Di:WO]; Miyuki Sawashiro as Renamon; and Ayumu Murase as Aliol, the Digimon Liberator full-dive guide. The cast is the strongest single selling point the mobile game has, and Bandai has not been shy about using it in pre-registration advertising.
The design is worth noting: the matches in Story Mode function as the actual tutorials. You learn the memory mechanic by needing it in a real duel rather than by reading a modal, and you learn archetypes by encountering them. For a physical game with as many interlocking systems as the Digimon Card Game, that is a considerably better onboarding route than a rules PDF - and it is the main reason to start in Story Mode rather than straight into ranked.