Pubsub (from 'publish-subscribe') is an XMPP extension (XEP-0060 that allows pieces of data to be published to 'nodes', and then automatically broadcast to any subscribers to those nodes. This is similar to technologies like RSS, except that instead of subscribers continuously checking for new data it is pushed to them in realtime.
Prosody comes with an internal pubsub service (mod_pubsub) that can be set up very simply:
Component "pubsub.example.com" "pubsub"
For a full list of options that can be used here, see mod_pubsub.
XEP-0060 is a very large document, and pubsub can grow to be a complex task. Different applications require very different feature sets. Prosody currently implements a baseline, the following features are supported (as of 0.9.0):