A relay is just a electronic switch that can take a low power signal and move a lot of current. Essentially, your mainboard can switch current for a heated bed but it's only rated for so much current before it burns out. You'll have to do some research to find out what that is. If you need to exceed that current you'll need a bigger switch (MOSFET) and you'll turn that on and off with your printer output.
What I highly suggest is that you use something called a Solid State Relay to turn wall power on and off to heat the bed. The 120v will never go through your board, your board will just power the relay.
If you watched the video I linked to you you probably saw Tom recommend 24v for the mainboard if you have TMC drivers. It'll be your best bet to get a 24v hotend and just run everything at that voltage (except, of course, your heated bed).
Alternatively you can keep the heated bed you have linked above and pump 500 watts (20 amps @ 24v) through your power supply and board/mosfet to get a less efficient and slower heating bed than you would if you went with an AC approach (120v). Make sure you have good thick wire everywhere with this, and if you have a bad connection there's a high chance of fire. If you found a equivalent bed (500w) for AC, you'd only be switching less than 5 amps, a much safer amount of current to be dealing with.
It looks like it would be good for you to keep doing research on this. All the info is out there (I learned it on the internet), and research always pays before you go and buy stuff. Just my two cents
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