A much misused term
. 'Inter' = between , 'Activity' = well, activity, doh.
Something that responds in ways that truly react to the user's input.
Clicking a standard link is only a shallow form of interactivity - this site is an example of much deeper interactivity, where the user's activity has many effects on the site which in turn have many various effects back on the user.
Interactivity is generally considered to be a good thing, but, in my experience, too much interactivity can be confusing for the user. We should strive for appropriate use of interactivity, rather than excessive use. Often less is more. You must balance the needs of the user, think 'useability'.