Marco,
The key is a licensing requirement. In other words - you have 120 days to evaluate the product and buy it. Once you buy it - you can just enter the key and not having to reinstall the product. In that way - the transition from Eval to Full is not disruptive to your users.
So the license prompt is there to remind you of the fact, that is all.
Please see the http://technet.microsoft.com/en-us/library/bb232170.aspx, specifically the "Evaluations and Product Keys" section. I am looking to have that added to Exchange 2010 documentation too, as it still applies.
NOTE TO ALL: it might take us a day or two to sort this out, but your servers will keep working. Even if the counter reaches zero (0) - there is no loss of functionality or service disruption that you will experience.