"What hempen home-spuns have we swaggering here,
So near the cradle of the fairy queen?
What, a play toward! I'll be the auditor;
An actor too, perhaps, if I see cause."
How Shakespeare uses it: Puck, a mischievous sprite, uses the term "swagger" to mean "insolent." It might have been a frequentative form of "swag," which means "to sway."
The word is also found in "Henry IV: Part 2" where Mistress Quickly gives a speech about super-aggressive men who visit her tavern, where the meaning of swagger suggests the meaning of boasting or bragging.
Additionally, the term is also found in "King Lear," where it most closely means "blustering." Although, here it is spelled "zwaggered."
Modern definition: Jay Z used "swagger" and "swag" in several songs back in the early 2000s. Soulja Boy also used the word — "she likes my swag." Since then, it has been often used in modern song lyrics.
Sources: "A Midsummer Night's Dream," Act 3, Scene 1, "Henry IV: Part 2," Act 2, Scene 4, "King Lear, Act 4, Scene 6