The kernel is basically the lowest level of software on any computing device.. It talks directly to the hardware and manages the cpu, memory, processes, etc.
From that you can see why a good kernel is important especially on mobile phones. A kernel with poor memory management and process management etc can lead to crashes, bad battery life, and a bunch of other problems.
The radio, apart from being the hardware piece, also needs a software component. That's what most people on here talk about when they say "flash the radio" etc. Another name for the radio software is baseband.
Android phones have several partitions on their flash memory where they store various stuff. Some of these are: the bootloader, radio, system for example. So your radio really can be replaced. When a new update for your OS comes out, it is usually prepackaged with the newest version of the radio. But if you're flashing different ROMs or different builds of the OS, you may have to flash different radios depending on where you live or how good your radio is performing.