Data are transferred between endpoints using Globus webpage https://www.globus.org/ (after login, choosing Manage Data -> transfer files), where you can choose between which two endpoints to tranfer data.
There are two types of endpoints: server and personal. You can choose add ‘Add Globus connect personal ‘ under manage endpoints to add create new personal endpoint: follow the instruction there. In this way, one can convert one local computer (laptop or a certain computer) into an endpoint. The server endpoints are usually for an organization such as Phytozome, which allows multiple users to use this sever endpoint to transfer files between the server and other endpoints. The mechanism is just sending transfer requests between endpoints, and the transfer will be done later (unsure who actually does it, maybe https://www.globus.org/).
OK. I hope that everyone will enjoy this new technology.