The name of this article is unofficial, or it uses unofficial terminology. It may change at any time as official terms are found or created.
A series is a group of multiple cards with similar name, artwork, and/or effect designs, but do not have a single shared name string that is mentioned by a card effect. Series are similar to archetypes, but archetypes are different in that they do have a shared name string mentioned by a card effect.
An example of a series is Digital Bug; there are cards with the "Digital Bug" name string (e.g. "Digital Bug Centibit"), they have similar visual designs, and similar card effects revolving around Insect monsters and Xyz Summoning, but there are no cards with an effect that specifically affects cards with the "Digital Bug" name string.
Series commonly, but not exclusively, comprise themed groups used by characters in the anime or manga. A group of cards may be a series in one media and an archetype in another. Examples of this include the "Shark" and "White" cards, which are both archetypes in the anime and manga, respectively, but lack any specific support in the TCG/OCG. Also, a member of a series may also be a part of an archetype, an example being the "Ultimate Insect" series, whose members are all also included in the "LV" archetype.