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"Gerbe" is a construct in homological algebra and topology. They can be seen as a generalization of principal bundles to the setting of 2-categories. "Gerbe" is a French (and archaic English) word that literally means wheat sheaf. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2.

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What is the geometric description of the set of isomorphism class of $G$-torsors over a site...

question, I should add that this whole conversation should carry over essentially verbatim in a higher-categorical context (for example, you could replace the group $G$ by $BG$, and then talk about $G$-gerbes
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