An Active-X control is simply a 'custom control' i.e. designed/compiled by a third party rather than a 'common control' supplied for use within whatever programming language you choose to use.
You will (most probably) find (several of) them in a lot of applications you use every day and are unaware of.
They are created by programmers to ease component re-use as they may develop a number of applications that require or can make use of that particular control.
The control can be 'signed' and thus you can be assured of it's integrity.
Bit techy bit if you want to understand more
read this