The kernel is the heart of the operating system. It is to Linux what an engine is to a car, or your brain to yourself.
The kernel is 'just another' program, but one that sits very close to your computer's hardware. It basically makes sure that all your computer's resources are available to user programs (that's everything that is not the kernel itself) and distributed fairly between them. Without the kernel, you could not work on your computer.
One of the nice things about the Linux kernel (every OS has one), is that you can indeed mess around with it. http://www.kernelnewbies.org
is a good resource for learning your way around it.