I'm having a really hard time wrapping my head around freesync and wether or not it relies on the cpu or the gpu, so my pc has a 7700k cpu and a nvidia geforce 1080ti gpu will it be able to utilize a monitor with freesync
It depends on your GPU. And no you can't use it with that setup. AMD and Nvidia both have different technology to prevent screen tearing. AMD has free sync and Nvidia has G sync. So if you want to use Free sync you will need an AMD GPU. The free sync monitors are also usually cheaper. But if you want an Nvidia GPU find a monitor that supports G Sync instead.
CPU doesn't matter...any gpu can 'utilize' either gsync or freesync displays. but as BSpboy said, the use of the specific type of refresh rate control is restricted to cards that utilize the specific technology(screen will still work fine, but you wont have variable refresh rate). While anyone could make a freesync GPU or monitor( i doubt nvidia will ever choose to, they like their tech proprietary), only nvidia can legally make a gsync cards and only those that have contracts with nvidia can legally aquire the rights and the gsync modules that are required to build gsync displays.
pcworld article addressing availability and pricing, if you want a little more