What is fabric in relation to a processor?
This sounds like a broadly interpreted term. But in the context of processors we (by we I mean my work environment of a major processor manufacturer) use this term to refer the whole infrastructure intended for a specific purpose, such as Data Fabric - which is consisting of the interconnect, control and arbitration logic involved in moving data of different types and representations between different processor blocks.
As reference I could find the AMD Infinity and Scalable Control Fabric description. Citation:


  Infinity Fabric (IF) is a proprietary system interconnect architecture
  that facilitates data and control transmission across all linked
  components