A kernel is a program that constitutes the central core of a computer operating system. It is responsible for translating the command into something that can be understood by the computer hardware. It is the first thing that is loaded into memory when a computer is booted up (i.e., started), and it remains in memory for the entire time that the computer is in operation. An executable, also called an executable file, is a file that can be run as a program.
The kernel is a part of an operating system. An operating system is something that includes a kernel plus quite a few lower-level applications (file manager, control panel, etc.) to make computers more user-friendly.
A distribution is an operating system packaged with distribution-specific patches which aim to make the system more usable.