Yes digital cameras still have a shutter they are still pretty similar to film cameras they replace the film with a sensor which record the light coming in through the lens.
Aperture: is the measure of how big an opening is made when the shutter is opened (the Click) a large lets alot of light in but has a a shallow depth of focus (only a little part of the shot is in focus) a small aperture only lets a little light in but has a large depth of focus most of the shot is in focus.
And just to confuse you further a small aperture number (f1.8 ) means the shutter aperture is really big (it opens really wide)
people who designed cameras must be such geeks.
To be honest I only got my head around apertures and focal lengths in the last year. and it is still kinda fuzzy.
on a canon the Aperature priority setting marked as AV and the shutter priority is Tv.
In this example you want a big fluffy fly in all in focus so you would use a high Aperture number so you will get the bits of the fly pointing towards the camera (Nearer) and the bits further away all in focus.
most pros will just use the auto setting on their camera for most shots
but this photographing flies could get quiet techy if you wanted it to.
here is a glossary on dpreview which is a great site.
hope that helps.