The kernel is the heart of Android, kind of like the gateway between hardware and software, and it controls all the hardware stuff directly such as the processor(s) and memory and the Tap2Wake feature.
Unless you have a specific need to switch, I generally recommend staying on the kernel included in the ROM. Some experienced flashers will stick with a specific kernel for all ROMs for a special feature or personal preference. On the G2 I haven't found any real reason or advantage to switch.
Remember kernels come in various "flavors", AOSP and CM based ROMs use a different kernel, also the G2 is kind of unique as we have 2 different display panels and it is possible to actually damage the screen with an improper kernel, I'm not going to really get into that but if you jump over to XDA there is lots talk on it and a tool to tell which display panel you have.
Flashing a kernel is simple, get the ZIP, start TWRP, flash, reboot... No wiping or formatting of anything is required (kernel does not directly use cache or dalvik), the device will either boot or not. If you flash a lot of kernels or test multiple ones, always go back to the ROMs original kernel first.
You will also need an app to set the kernel options you want, some kernels have there own app, some use generic "kernel tweaker" apps from the Play Store, read the kernel thread to see which the Dev recommends.