Wiktionary
n. 1 (context set theory English) The set of functions from the indexing set of an indexed family of sets to the union of the family, whose values at any given index lie in the set indexed thereby. 2 (context mathematics English) The generalization of direct product (1) to arbitrary categories.
Wikipedia
In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions.
Examples are the product of sets (see Cartesian product), groups (described below), the product of rings and of other algebraic structures. The product of topological spaces is another instance.
There is also the direct sum – in some areas this is used interchangeably, in others it is a different concept.
Usage examples of "direct product".
A good part of the officer's code is based on this mental image of chivalry and is a direct product of the knight's code.
The euphoria of the big rock festivals was a direct product of this phenomenon.