A kernel is the middle-man between your software and your hardware, put simpy.
4.4 is a version of the Linux kernel (what "Linux" actually is; the kernel), where the first 4 is the major release version number, and the 2nd 4 is the minor release, I believe. There's surely more to it, but I'm not all that well versed in version schemes.
There's a patch number, as well. Typically, the big distros (Debian, Arch, Ubuntu, etc) will patch the kernel, to keep it up to date as far as security goes, and likely also patching any stability and performance issues. However, the 4.4, for example, indicates that the drivers -- modules allowing your hardware to function -- or versions thereof, within the kernel, were upgraded over versions lower than 4.4, such as, for example, 3.8, or 2.4.
Typically, the newer (bigger the number) the major/minor release version of a kernel, the newer the hardware it'll support, which is an important factor to keep in mind when choosing a kernel version to install and run. Sometimes newer kernels drop support for certain hardware, leaving some people to need an older kernel to continue running their toaster, thus those too are maintained (patched).
dave8671 wrote:If the kernel does not boot how would I fix it? Which kernel is for this hardware right now I am using the 4.10 would it be 413.x
If, after loading up a different kernel, the system doesn't boot or operate correctly, your best bet is to reboot the machine, spam the Shift key (or Esc as some have reported) to get to the GRUB menu, then, when there, select the menu option begginning with "Advanced options for", then select the kernel you were using before, when things worked. Once that's done, you should be booting into your machine like normal, then just remove the kernel which didn't work for you.
I have no idea which kernel is for your hardware -- I don't even know what your hardware is.