This purely crystallographic concept has few precise definitions useful for gemologists. We propose one that is applied to minerals. The concept of twinning is broader, as it concerns the notion of network, which is not per se limited to crystals.

(proposed) DEFINITION
A regular association (grouping) of two or more crystals of the same species with different crystallographic orientations, according to geometric laws directly related to the -exact or approximate - symmetry of the crystal network.

see for example
(and many other websites)

Several categoires of terminologies have been attached to the notion of twinning and twinned crystals. For example:

    Genetic : growth twin, deformation twin, transformation twins, etc.
    Morphological : Contact or penetration, reticular, butterfly, cross, heart, knee, etc.
    According to the minerals in which they are most commonly found: fluorite twin, spinel twin, etc.
    According to classic sources: Dauphiné twinning, Baveno twin, Carlsbad twin, etc.
    According to the symetry of the species: merihedry, pseudomerihedry, etc.

Additional information