If #92;mathbf#123;A#125; is the category of sets, then #92;Pi#95;Bf is (up to isomorphism) the usual Cartesian product of the fibres A#95;y. If #92;mathbf#123;A#125; is a category of spaces and smooth maps, then an element of #92;Pi#95;Bf will have values varying smoothly in the indices, while if #92;mathbf#123;A#125; models data types and computable functions the values will vary computably.
Source: wiktionary