A context is a bundle of settings. Among the settings in the such bundle are
Filters (for example I have a context "To Be Estimated" which filters out everything which should not be estimated (bugs), is already estimated or is not ready for estimation (not clear enough).
Sorting: Only when sorting is done by a rank column you can use the Context for prioritizing issues.
Highlighting
About the on the fly context the Greenhopper wiki is quite helpful I think:
GreenHopper comes with 2 built-in contexts:
'On the fly' context — A non-deletable context that will allow all logged-in users to build new contexts (See the 'Creating a New
Context' section below). Any changes that a user makes to this context
will only persist for the current session and will not be saved.
'Default' context — A non-deletable context that only people with the
'Administer Projects' permission can edit and that is shared with all
users and anonymous users (if your project is public). It is very
important to note that editing this context will affect all users that
use that context.