To use it, you just type "@google," and then tap the assistant when it pops up. You can then ask for a meeting date or airline reservation, for instance, and it will privately show you any of the information that it can find. From there, you can tap "share now" to show the info to other parties in the Allo chat.
That makes it easy to quickly give pals a contact number without having to look it up, for instance. Or, if you're trying to coordinate a work trip, you can have Google Assistant give your hotel reservations to colleagues during a chat.
Google Hangouts, the predecessor to Allo (and still the preferred chat app of many Google users), has had similar capabilities for a few years now -- it'll even listen in to conversations and let you share your location if someone asks where you are. Facebook recently launched similar capabilities for its "M" Messenger AI assistant, too. It's debatable whether they'll make you more productive, but Google needs to draw interest to Allo however it can.