Look at it this way :
a rom is like a ps3 game and your phone is the ps3. You have a stock rom which is the one your phones has out of the box. Then you have custom roms built by ppl/devs which are lighter, debloated (all the crappy apps have been taken out), faster, that you, under the right circumstances, can load into your phone and it may feel and look like a whole new OS.
A kernel , to my understanding, is pretty much what brings everything together, manages it, and makes it work. Youll hear ppl talk about kernels overclocked to a certain speed which means itll run faster, and undervolted which means they, in thoery, will consume less power/battery.