WebLogic Server is an application server software that runs Java EE applications and provides services like clustering, load balancing, and failover. It sits in the middle tier of a three-tier architecture, between front-end clients and back-end databases. The presentation discusses WebLogic Server's role in running major Oracle applications like OBIEE, E-Business Suite, its administration using tools like WebLogic Administration Console and Fusion Middleware Control, and how it fits into Oracle's technology stack.