I found that minutephysics video. I'm not sure how useful its description of what the Higgs does as causing a particle to bounce "back and forth at the same time" is , but it is very hard to try to describe these quantum effects in familiar language.
I'm not quite sure what your proposed explanation of the c
2 is. The argument for why there must be that conversion factor to go from mass units to energy units was developed by Einstein long ago. It's really rather simple, especially if you start from the previously known fact that for light E=pc, where p is momentum. Any good beginning book on special relativity should have this argument early on.
Mike W.
(published on 04/09/2013)