That file format is high definition video files.
I think you'll find that most Core2Duo and Core2Quad CPU based PC's with the latest graphics card will easily run those videos.
The resolution is usually 1080 or 720 on those file formats.
I downloaded some videos from Microsoft a few weeks back and my PC had no problems at all running them - I use a E8200 CPU (that's 2.66Ghz x2) with 8800GT graphics card and 2Mb RAM.
Just go to PC World, John Lewis, Curry's, Comet, etc if you want to walk in or try a host of online stores such as Dell.
Big question now is what your budget is.