BI - Business Inerlink - This is peoplesoft object that behave like DLL. If you have to modify something on other application, like some of directory that controls single sign on Business Interliks are used.
CI: Component Interface - This is used to validate any entries in peoplesoft system. say some third party system sent one inbound file and based on the data in inbound file you want to insert row in peoplesoft, you also want the current validation at component (say xyz) to take place. Then create a component interface with xyz component. read the inbound and process it through newly build CI.
IB - Inegraion Broker - This is integration point of peoplesoft with all other peoplesoft and thirdparty application that uses Messaging.