The kernel acts as a mediator between your programs and your hardware. First, it does (or arranges for) the memory management for all of the running programs (processes), and makes sure that they all get a fair (or unfair, if you please) share of the processor's cycles. In addition, it provides a nice, fairly portable interface for programs to talk to your hardware.
There is certainly more to the kernel's operation than this, but these basic functions are the most important to know. All Linux distributions share the same Kernel source codes, There are different versions of Kernel and the version you have can determine what you can do with the Linux distribution you have. Kernel can be upgraded.