IBM Cloudant is a database-as-a-service based on Apache CouchDB. It's a JSON document store whose storage mechanism makes it great of having multiple, partially-connected data sets e.g. a copy "in the cloud" and a copy on a mobile device.
PouchDB is an open-source database that can run in a browser or in Node.js that speaks the CouchDB replication protocol. It can be used to store data on the mobile device, optionally replicating data to the cloud (CouchDB or Cloudant) when needed. This practice is often called "Offline First" development - getting your app to store and retrieve data in a local data store to give the user 100% uptime, even when there's no network connection.
Hoodie and Meteor are opinionated application development frameworks. You can use their scaffolding to build your applications. They in turn may use PouchDB for local storage and/or Cloudant or CouchDB as a server-side store.