When Briar runs on your phone, it starts a Tor instance and creates a Tor hidden service directly on the device. Your Briar identity is literally a .onion address. Contacts connect to you by establishing a Tor circuit to your .onion address; you connect to them by establishing a circuit to their .onion address. There are no servers in the communication path.
This architecture has a critical implication: communication is only possible when both parties are simultaneously online. Briar has no message queuing infrastructure because there is no server to queue messages on. If your contact is offline, messages cannot be delivered until they come online. This is fundamentally different from Signal, Session, WhatsApp, and email - all of which store messages on servers for asynchronous delivery.
For the right use cases, this limitation is acceptable or even desirable. A journalist meeting a source in the same city can use Briar for real-time communication with no server infrastructure that could be subpoenaed. The meeting communication exists nowhere except the devices of the two participants. Server-based messaging systems leave traces on servers even when messages are deleted from user devices.