I am a new linux administrator and noticed one of our licenses says "Spectrum Scale Standard Client Socket Annual"... I am curious if someone can explain to me what a "socket" is? Is it a server or the cpu sockets on a motherboard? 

Welcome to the world of braindead "enterprise software" licensing.

Perhaps this FAQ answers your question:

https://www.ibm.com/support/knowledgecenter/STXKQY/gpfsclustersfaq.html

If virtualization is involved, prepare to have much fun trying to figure this out.