What exactly do mathematicians mean when they refer to "the data" involved in a construction?
I've encountered this many times and I can usually figure out what's going on, but I am curious about the terminology, how it was introduced, and its connotations.
A concrete example: In pages 35-6 of "Differential Geometry" by R.W. Sharpe, there is a section entitled "Construction of Bundles". The author outlines three conditions that hold for a given $G$ bundle, and then later refers to these three conditions as "data" from which a $G$ bundle can be constructed. This usage confuses me.
Is there a semantic reason why standard words, like "component", "part", or "constituent" are not used?