That little cylinder is called an air gap cover. An air gap is sometimes needed in DW installation. You need to find out from your plumber, contractor, or DW installer if your installation will require an air gap. If it will, you will probably want to order a cover.
I don't know anything about what they are or what they do. Sometimes they are required by code, it has something to do with how high the drain loop for your DW can go, I think.
If you go over to the appliance forum there is lots of information about air gaps, or you can do a google search on 'gardenweb air gap".

What you don't want is for the dirty water from your DW to back up into your clean water supply. One way to do this is to install an air gap on the sink top:

Another solution is a "high loop" in the plumbing of the DW:

Clearly, the high loop is what one would choose by preference to having that junky cylinder sitting out on the sink. Unfortunately, some states' codes require the air gap.

I have an air gap (Calif., old DW) and it's just not as tragic as some make it out to be. I think they all look pretty much alike and you should be able to pick up one with your choice of finish locally.