I'll confess that the Club Penguin phenomenon is somewhat indecipherable to me. As someone who is neither a kid nor has kids, that's probably OK. But if you have children of a certain age, you might be familiar with the online site, a Disney property filled with simple browser games and penguin-themed customization portals. Now there's an Android version, for better or worse, aimed at taking the experience on the go.
I suppose that Club Penguin is technically a massively multiplayer online game, though "game" seems to be stretching the definition a bit. Kids create a penguin avatar, engage in some extremely basic winter-themed games, and decorate their personal homes ("igloos.") There are also portions of the 2D world reserved solely for interacting with other players, though given the kid-focused nature of the game, these interactions are highly limited to prevent any vulgarity or the revealing of personal information. Ancillary activities (and the ones that seem most popular) are decorating avatars and igloos and taking care of Tamagtchi-style virtual pets called Puffles. They're basically Tribbles, without all the breeding. Monthly updates add new themes that keep things interesting.
Club Penguin is technically free to play, but most of the more advanced features are hidden behind a subscription paywall. A month of access for your kid will cost $7.99, or slightly less if you buy longer subscriptions. That would be fine, but it looks like it's possible to buy subscription extensions from within the app itself via Google Play in-app purchases. That kinda sucks, Disney - even with all of the security measures that have been put in place for in-app purchases, it's still way too easy for kids to access IAP in a "kids-only" game. I'm of the opinion that this sort of thing should be accessible only from the web with a credit card. The following disclaimer from the description doesn't exactly inspire confidence, either.
Before you download this experience, please consider that this app contains in-app purchases that cost real money, push notifications to let you know when we have exciting updates like new content, as well as advertising for the Walt Disney Family of Companies. Children should always ask their parent or guardian to download and play. WiFi is needed for some features. Network or Carrier data fees may apply if WiFi is not connected.
It should also be noted that while the Android version of Club Penguin has a lot of the same activities as the web game, it's not a complete replication, and you might not be able to do everything on your phone or tablet that you can elsewhere.