Nowadays this word's use is restricted to the description of a class of subatomic particles. Many years ago, though, long before anyone had even thought of such abstract weirdness as overlapping wave functions and quantized angular momentum, it was an alternate spelling of bosun, which is itself a shortened (and more phonetic) spelling of boatswain.
This, apparently, was still the case in 1913 C.E. There used to be a Webster 1913 writeup in bosun suggesting that the reader see boson for more information. I naturally thought old Webby was a bit off his rocker, and added a writeup there to the effect that a nautical officer simply wasn't the same thing as a subatomic particle in any version of the English language I was familiar with. Eventually both writeups were replaced by a firmlink.
I think the 1913 editors of Webster's dictionary had been relying more on Renaissance literature than on more recent developments in the language. Bosun seems to have been in use among English-speaking navies at the time, and boson was essentially an archaism, since the Pauli Exclusion Principle hadn't yet been formulated. However, the Renaissance-era mariners of The Tempest used the older spelling. From act 1, scene 1 of that play:
BOATSWAIN. I pray now, keep below.
ANTONIO. Where is the master, boson?
BOATSWAIN. Do you not hear him? You mar our labor; keep your cabins; you assist the storm.
Needless to say, Shakespeare's characters pronounced the word differently than do present-day physicists.