Live mode sends your data to the Kappa322's server (or the server you set up, check Github for src) and downloads the data of your squadmates to display for you. This is the way you share your statistics with others.
To toggle Live mode you open settings with + + and navigate to the extensions tab then to Healing_Stats and choose enable live stats sharing (a shortcut should be available in future releases). This will automatically connect you to the default server and search for data to download and send.
In certain cases live sharing can impact the network quality, so do keep it in mind when having network issues. With good enough internet you shouldn't even notice a difference, but for highly limited plans it may be a major stutter contributor. Personally, I toggle it on only when we're having issues and I need to figure out what's up with the heals. Although developer agreed on adding a low bandwidth mode in the future releases, so if you're having issues with the addon right now, look forward to it!
The general idea is that the addon shouldn't send more than 20 events per second per player.
This means that your upload will be at max equal 64b * 20 = 1280 b/s =~ 1.3kb/s
While your download in a squad of 25, with two supports per party using the meter would be at max 64b * 20 * 10 = 12800 b/s =~ 13 kb/s
While your download in a squad of 50: 64b * 20 * 20 = 25600 b.s =~ 26 kb/s
Overall usage should be quite often lower due to less events happening on average, although there may be additional data usage from the framework used. While this is very small amount by itself, you need to remember that both GW2 and Discord (also Spotify, Youtube and anything else you running in the background) will use your network as well. If you have multiple people using low-speed Internet at the same time, it may start struggling and causing you performance drops.