This Higgs, giving mass to all elementary particle by so called "Higgs mechanism", was unable to find in experiments after P.Higgs proposed this in 1960's. Thus this remained as the missing "piece " in the Standard Model. Later someone, because of the very same reason that i mentioned above, called it as God Particle eventhough it has no connection with God!
The fluctuations of a scalar field in the early universe could have created thanks to the inflation the major structures we see today (galaxies clusters...). If that scalar field is THE Higgs field, then it is somehow responsible of how our universe look like, that is one reason what it had been quoted the God particle, but DO NOT take this nickname seriously, it is more a physicist's joke.