You buy a plan for the place you are going, install the eSIM on your phone before you fly, and it connects to a local mobile network when you land. We are not a mobile network: the plan runs on the networks of local operators in each destination.
It carries mobile data only. Your own number stays on your own SIM, so calls and texts still reach you at your carrier’s usual rates.
For most plans the days start when the eSIM first connects to a network at your destination, not when you buy it. That is why installing at home on wifi is the easy way: you land already online.