A mail client is a program that is installed on your PC and becomes the main program you use to do your emails. This could be Outlook, Windows Live Mail and so on.
When you click on the website link it tries to start this email client program so you can send the email.
But as more and more people do their email via the web in hotmail or googlemail or yahoo mail many of us dont have an email client program installed on our computer, so there is no program for the web site to start.
Often you can find the email address somewhere else on their web site, or look at the properties of the link and see what their email address is.
Then you can just send an email to them in the normal way with our normal email program, and just type in their email address, or copy and paste it from their web site.