what use case is there for graphql? and what does meteor have to do with it?
GraphQL basically allows to build your backend as a well defined API. Then, you can query it from anywhere. It has a good query language and some nice tools like GraphiQL - https://github.com/graphql/graphiql
Meteor is a full stack. It has no direct relationship(or cannot compare with) GraphQL. Meteor also a realtime framework, but GraphQL does not address realtime aspects (yet).