In standalone JIRA, if a component has a description the user can mouseover the component and the tooltip says "<component> <description>". In JIRA OnDemand it only shows the component and not the description.

It does show the description when just on the view issue page, though it could be made a bit easier to read... if I have a component called "Foo" with the description "This is a description of component Foo", the tooltop says "Foo This is a description of component Foo". There should be a dash or colon or something to separate the name and description.