We couldn't go into everything in the video (it was already too long!), but the piece you're missing is Meteor.methods(). This lets you define methods, which are functions that the client can invoke on the server by calling Meteor.call(). If you choose to also ship the code for these methods to the client (it's optional) then you'll get full latency compensation like we talk about in the video. (This means that Meteor can latency-compensate arbitrarily complex functions, like "read this record, then add 2 to X if this field is false, else create a new record Y.")
In fact, every Meteor app already has an API :) Your Meteor client can connect to any other Meteor server by calling Meteor.connect(), and can then subscribe to any realtime datasets that that server is publishing, or invoke any methods available on that server. This is done with a protocol called DDP, but we could map DDP to REST fairly easily.
What about a non-Meteor client connecting to a Meteor server? Does that client have to understand DDP, or is that what you mean by "we could map DDP to REST" - there's no support for non-DDP clients now, but it's planned?
The latency compensation and Meteor.call() interface sound great, but what I understood by the GP's question about an API was "how can other clients besides mine talk to my app?".