Hi Craig,
The Kernel is the central program which acts as an interface between SAP application and operating system.
The Kernel consists of the executable programs that reside under the path "/sapmnt/<SID>/exe" (UNIX) or \usr\sap\SID\SYS\exe\run (Windows)
These files help startup the R/3 system, initialize the memory, create buffers and start managing the requests from users and effectively utilizing of hardware resources.
The kernel is also responsible for starting and stopping all the application services like dispatcher, message server, collector etc.
For more information, please check:
SCN blog:
http://scn.sap.com/community/netweaver-as/blog/2015/05/29/information-on-sap-kernel-and-upgrade
Internet document:
http://www.guru99.com/sap-kernel.html
Thanks and best regards,
Shi