DWC is a game which is part Digimon, Tamagotchi, and Pokemon Ranger, with elements of Monster Rancher and... you get it.
There is no plot to this game, and as such, I would recommend that if you are getting this game, you do it with a friend, and you both better love Digimon. Because of the shallow nature of the game, a love for Digimon helps keep you interested consciously, and I recommend a friend because multiplayer probably also encourages your continued play (in a similar fashion to Pokemon; you keep training to get better to beat your friend/sibling... although you maybe only battle that person once or twice in the hundreds of hours you spend training).
What you do in this game is simple. You feed, train, and clean up after your Digimon in a very Tamagotchi like fashion. While doing this, you frantically move your Digimon from cage to cage where they learn different skills which result in stat boosts, which affect your Digimon's branched evolution tree in ways I have yet to personally discern, and as a new game there is not yet a walkthrough on GameFAQs leaving me with my rag-tag team of random Digimon. When you have enough space for more Digimon, which you get by winning Title Match Tournaments, you go out and hunt for more, by circling them with your stylus and then yanking them until they get too tired and you can bag and tag them. (Unlike PKMN Ranger, you only need to circle them once, but you need to pull on them a fair bit, which is worse then Ranger's incessant circling). You can also shoot at them, bomb them, and bait them, and a whole slew of things I've yet to unlock, I'm sure, but the idea is the same.
And then there are the tournaments themselves, and the point of the whole thing. Essentially, you hope you've trained your soldiers well enough, because you choose three, select their battle mode, and set 'em loose; the battle is fully automated and often frustrating to watch.
Still, the whole experience is rather fun and rewarding, in my opinion; you have to have conquered a number of pointless games before it to be able to deal with something of this nature (Pokemon, Monster Rancher, and previous Digimon games come to mind) but if your a fan of the series, I highly recommend this unexpected gem.