So I messed around with this a bit tonight. It's not very elegant (and manual), but there are a couple ways to do it.
As Fitbrit said, you can get the info from TVDB. Maybe we could have this info pulled automatically please?
For now, I use the following Managed Link to access it:
<Link version="1.2">
<Item Name="Name">TVDB</Item>
<Item Name="Action">1</Item>
<Item Name="Base URL">http://thetvdb.com/</Item>
<Item Name="Search URL">http:////thetvdb.com//?string=Hexify([Series])&searchseriesid=&tab=listseries&function=Search</Item>
<Item Name="Filter">[Media Sub Type]=[TV Show]</Item>
</Link>
The first way I tried, I changed my Series view Details from Series -> Season to Expression -> Season using the Expression [Series]: [Series Description]. This works, but there is only room to display the first couple sentences of the description. Some list styles look better than others too. Perhaps you could mess with the skin to make it display more?
The other way that looks pretty decent was to add Series Description to the file info panel. Tools -> Options -> Theater View -> Appearance -> Customize file info panel. I added Series Description to the TV Show template, and I put it at the top of the list selecting Show: Always show and checking Hide when value is empty. With this option, you need to click into the first Season to see it, but you would only have to tag the first Episode of the first Season with the Series Description.
I'm sure there are others here that could probably clean this up better, but at least it's a start to show it is doable.