Lets your modules stay in touch with each other.
Modules are intended to be modular and therefore to work on their own. So why do we need to connect our modules with each other?
TerrificJS modules most often have a visual counterpart that – due to the nature of frontend – necessarily has to be rectangular. So sometimes you will have to split up a functionality across multiple modules.
Thinking of filtering of e.g. twitter messages, you could have a module Messages for displaying the messages and another module Filter for selecting the appropriate filters. Additionally this helps you to keep modules simple and to split the complexity in smaller parts.
Regarding the implementation of connectors, everything you need to know has already been covered elsewhere.