Don Thousand uses this card in both of his Duels in the anime. In both cases, he activated it at the beginning of the second turn of the Duel, taking the first turn and doing nothing whatsoever in order to meet the activation requirements of "Numeron Network".
When active, this card appears as a physical network of lines and tunnels on the Earth, originating from a black sphere of energy that holds the actual "Numeron Network" card. Astral and Eliphas (and presumably, other Astral World and Barian World denizens) are able to travel through the network - conversely, the network can project tendrils of black energy to obstruct them. Don Thousand can sense intruders' presences in the Network and enable communication between different parts of it by projecting images of the areas in question.
In the Yu-Gi-Oh! ZEXAL anime
In episode 138, Don Thousand uses this card during his Duel against Mizar. He activated this card on Mizar's Draw Phase through its first effect, then used its second effect to activate "Numeron Spell Revision" from his Deck, negating the effect of Mizar's "Dragon King's Demise" and activating "Card of the Dragon King" instead, causing Mizar's life points to drop to 0. Since neither of his cards were shown activating, it appeared to everyone that Don Thousand had somehow defeated Mizar without playing a single card - the existence and effects of the cards were only explained by Don Thousand during his subsequent Duel with Yuma and Nash.
Don Thousand activates this card at the start of his Duel with Yuma and Nash. He uses its effect to activate "Numeron Xyz Revision" to destroy Yuma's "Number 39: Utopia", summoning "Ganbara Knight" instead. At this point, Don Thousand explains the effects of "Numeron Network", and how he used it in his Duel against Mizar. He also reveals that this card has merged with the Earth through the power of the Numeron Code (since he has total control of the Barian World, which has merged with the Earth).
In episode 139, Don Thousand activates "Numeron Calling" since he controls this card, allowing him to summon "Number 4: Numeron Gate Catvari", "Number 3: Numeron Gate Trini", "Number 2: Numeron Gate Dve", and "Number 1: Numeron Gate Ekam". He proceeds to attack "Ganbara Knight" while using the Gates' effects to double their ATK after every battle; he explains that this card allows him to use his "Numeron" monsters' effects without detaching Xyz Materials. At this point, Astral leaves Yuma to Duel while he enters the Numeron Network in search of the card. Later, Thousand uses this card's second effect to activate "Numeron Spell Revision" from his Deck, negating Nash's "Aqua Jet" and replacing it with "Surface". However, Nash later reveals that he intended for Thousand to negate "Aqua Jet"; since this card's effect can only be used once per turn, he is free to initiate his true strategy of summoning both "Number 101: Silent Honor ARK" and "Number C101: Silent Honor DARK". After Nash's Battle Phase, Astral finally finds this card at the center of the Numeron Network. He brings it out of the network and places it on Thousand's field; however, Thousand reveals that destroying this card will cause the network's energy to backfire on itself, destroying the Earth in turn. Nonetheless, Nash uses the effect of "Depth Eruption" to destroy all cards on the field, including this one. Astral absorbs the energy of the collapsing Numeron Network, intending to sacrifice himself to save both worlds, but Eliphas intervenes. As he begins absorbing the network's energy, he throws a card to Astral, teleporting him out of the network before it explodes.
In episode 140, Don Thousand's "Number C1: Numeron Chaos Gate Sunya" returns to the field after banishing itself by its own effect; however, since this card is no longer on the field, it destroys itself without inflicting damage to Yuma and Nash. Don Thousand proceeds to activate "Numeron Chaos Ritual", treating this card and his four "Numeron Gate" monsters as Level 12 monsters for an Xyz Summon. He then overlays his five Materials to Chaos Xyz Summon "Number C1000: Numeronius".