In that context it's talking about a Coat of arms - Wikipedia, the free encyclopedia . You'll notice that pubs called The <something> Arms have a shield for a sign. Originally, it presumably marked the family of the publican; I had a cousin named Charles Slaughter, and he owned a pub called The Slaughter Arms (which had been in the family for generations). I expect some pubs, though, just pick that name because they feel like it.
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