In algebraic geometry, given a smooth algebraic group G, a G-torsor or a principal G-bundle P over a scheme X is a scheme (or even algebraic space) with an action of G that is locally trivial in the given Grothendieck topology in the sense that the base change Y × X P {\displaystyle Y\times _{X}P} Y\times _{X}P along "some" covering map Y → X {\displaystyle Y\to X} Y\to X is the trivial torsor Y × G → Y {\displaystyle Y\times G\to Y} Y\times G\to Y (G acts only on the second factor).[1] Equivalently, a G-torsor P on X is a principal homogeneous space for the group scheme G X = X × G {\displaystyle G_{X}=X\times G} G_{X}=X\times G (i.e., G X {\displaystyle G_{X}} G_{X} acts simply transitively on P {\displaystyle P} P.)
Look, there's even links to the sub-terms:
("algebraic group" article): In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.
("action" article): In algebraic geometry, an action of a group scheme is a generalization of a group action to a group scheme. Precisely, given a group S-scheme G, a left action of G on an S-scheme X is an S-morphism
("principal homogeneous space" article): In mathematics, a principal homogeneous space,[1] or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively (meaning that, for any x, y in X, there exists a unique g in G such that x·g = y, where · denotes the (right) action of G on X). An analogous definition holds in other categories, where, for example,
Really, all you have to do is read the article carefully and follow the links to unknown terminology if you can't immediately intuit its meaning. However, it's only just basic category theory, really.
(yes, guys, /s).