In the Assassin's Creed series, Abstergo Industries is the company that publicly sells products while secretly serving the Templars.
Abstergo is one of the franchise's most important modern-day institutions. It operates as a large multinational corporation with interests in technology, medicine, entertainment, and other fields. Behind that public image, its leadership is connected to the modern Templar Order and seeks to use historical knowledge and Pieces of Eden to impose its vision of order.
The Animus, the machine that lets users experience genetic memories, is developed and controlled through Abstergo-related operations. In later games, Abstergo Entertainment commercializes Animus memories as interactive entertainment, creating a fictional explanation for how players can experience historical adventures.
Abstergo Entertainment is therefore a real subsidiary within the fiction, but it is not the answer to the broader company question. The company name “Abstergo” comes from a Latin verb meaning “to cleanse” or “to wipe away,” a fitting reference to the Templars' ideology.