I don't think of myself of the ultimate autority on Genesys products but maybe this would help a little.
I like to think of Genesys products as a collection of software to assist in Call Center management. Genesys products are divides in a few categories like Inbound Suite, Outbound Suite, T_Server FrameWork.
The basis of Genesys is to provide connection between your Voice Network and your Data Network. The TServer is the heart of the software. I act as a "SPY" on your voice equipment (PBX) and reports every status of every agent phone, and other telephony ressource like ACD, RP, etc. TServer generates event that can be trap by an Application on your network and perform action based on these events. The most popular application developped around Genesys is Screen Pop. Screen Pop allows you to synchronize caller information on the Call Center Agent desktop at the same time that the call is forwarded at the agent.
Genesys includes software for the following specialize functions :
Intelligent call routing,
Statistical reporting
Outbound Campaign for telemarketing
Real Time call center monitoring
And few more other things
Genesys is somehow a sophisticated software, but not impossible to master.
I know this is not much, but is a start, EMail me if you have other specific questions.