Overview:

WebLogic servers are called middleware or application servers. They are called so as they act as a middle layer between the front end user interface and the backend database.

WebLogic servers host the applications or the business logic required to perform any action. For example, when you click a button on webpage, the request goes from your browser to the WebLogic server, the application deployed decides what action is to be taken for the request, queries database and gives the response on your screen.

WebLogic servers are owned by Oracle. Its rivals are JBoss servers by RedHat and WebSphere by IBM.
Oracle WebLogic Server is a Java EE application server currently developed by Oracle Corporation. Oracle acquired WebLogic Server when it purchased BEA Systems in 2008.