Ok, it
is pretty much very complicated. Even most physicists would need a couple of minutes just to figure out how to parse a sentence on how to describe it.
a) What it comes down to however, oversimplified, is that it is a particle that a theoretical physicist named Peter Higgs proposed to exist, with hugely complicated math, to try and explain why matter and mass came to be. Somewhere a physicist is cringing at my explanation and he is welcome to correct me. But there you go.
b) This discovery means(if it is the Higgs, it's not confirmed yet

) that the Standard model of physics is pretty much correct. It also has some other implications, which are to vast to try and answer in a post.
It also might bring back talk of the ether!
. Tesla would be ecstatic! LOL Or not! Higgs fields and all! We'll see.
c) Immmense. It already has! Even if it wasn't discovered at all! You see this WWW thing we're using?
Say thanks to CERN for that.
The search for the Higgs, in a way resulted in My Broadband.co.za coming into existence. How's that for impact? Research and development into seemingly-conceptual sciences(but physical nonetheless) like this is so vast and influential it seems invisible to the everyday man like us. Like space development. But it's there and it's immense, simply because of the supporting technologies it fosters and develops. And you can bet your ass that all that networking, data storage and processing technologies that they developed will find their way to our data centers in a few years too.