The Higgs boson's nickname "the God Particle" was solidified upon its discovery, namely as a result of the popular media. The origin of this is often connected to Nobel Prize-winning physicist Leon Lederman referring to the Higgs boson as the "Goddamn Particle" in frustration with regards to how difficult it was to detect.
Business Insider says that when Lederman authored a book on the Higgs boson in the 1990s the title was to be "The Goddamn Particle" but the publishers changed this to "The God Particle" and a troublesome connection with religion was drawn, one which bothers physicists to this day.
Still, it's hard to overestimate the importance of the Higgs boson and the Higgs field in general, as without this aspect of nature no particles would have mass. That means no
stars, no planets, and no us — something which may help warrant its hyperbolic nickname.
In 1964, researchers had begun to use quantum field theory to study the
weak nuclear force — which determines the atomic decay of elements by transforming protons to neutrons — and its force carriers the W and Z bosons.
The weak force carriers should be massless, and if they weren't this risked breaking a principle of nature called symmetry which — just like the symmetry of a shape ensures it looks the same if it is turned or flipped — ensures the laws of nature are the same however they are viewed. Putting mass arbitrarily onto particles also caused certain predictions to trend towards infinity.
Yet, researchers knew that because the weak force is so strong over short distance interactions — much more powerful than
gravity — but very weak over longer interactions, its bosons must have mass.
The solution proposed by Peter Higgs François Englert, and Robert Brout, in 1964 was a new field and a way to "trick" nature into breaking symmetry spontaneously.