The title "arms and the man" is taken from the opening line of Virgil's Aeneid, "arma virumque cano" (Latin for "I sing of arms and the man"). In Virgil's poem, it signifies that the work belongs to an epic tradition, telling a tale of an ancient hero and brave and heroic deeds.
The "man" of the phrase is Aeneas, the Trojan prince, who, fleeing the fall of Troy, became the mythical founder of Rome. When Shaw was writing his play, every member of the audience was likely to have studied Virgil in school and the educated audience members would have read Virgil in Latin, a language at this period still required for admission to Oxford or Cambridge universities.
Shaw is using the phrase somewhat ironically as Captain Bluntschli is a pragmatic mercenary rather than a legendary figure. On a more profound level though, Shaw is suggesting that his play represents a deeper reality of war and its effects on participants and civilians than epic.