Most phones made in the last few years can use an eSIM. That includes iPhone XS and newer, Google Pixel 3 and newer, and recent Samsung Galaxy S and Note models. Your phone also needs to be unlocked, meaning it is not tied to one home carrier.
Here is a quick way to check before you buy. Open your phone settings and look under Mobile Data or Cellular for an option that says Add eSIM or Add Data Plan. If you see it, you are fine. You can also dial *#06# on the keypad. If a number called an EID shows up, your phone supports eSIM.
Once you land, your MegaEsim plan locks onto the Claro network in Uruguay. You keep your normal SIM and home number working at the same time, so friends and family can still reach you.