Kernel software and drivers are software modules and components that make up the ‘guts’ of a computer operating system such as Windows, Apple OSX and Linux.  It is mostly all the software that is included with the operating system you don’t directly use or see. This software controls the hardware (computer chips, displays, keyboards, network, etc.) and enables the sharing of those hardware components among all the applications executing on the computer. It also manages the execution (startup, closing, and shared interaction) of the multiple software applications on the computer. Kernel software and drivers use unique software architectures and technologies that aren’t typically used by application software.
For more information:

• A description from the Linux Information Project