Meteor dev here. If you're writing a Meteor application, you need a realtime database. Otherwise, Meteor can't make the page update in realtime, because it can't find out about database changes in realtime.

Firebase is a realtime database that you could use with Meteor. The database we use in the Meteor video is MongoDB with Meteor's 'mongo-livedata' package, which adds some realtime glue to Mongo. But there are many potential advantages to using a database that is designed from the ground up to be realtime, and we're very excited that the smart guys at Firebase are taking this on. We predicted that this would happen eventually, but we had no idea it would be so soon.

(If you don't like the word realtime, please s/realtime/reactive/)