The short answer
The PSTN is what "a phone call" means. A voice agent that reaches real phone numbers terminates on it, which imposes constraints no browser-based demo reveals: 8 kHz narrowband audio, lossy codecs, carrier-level call setup delay, and a routing and numbering system with regulatory obligations attached to it.
In detail
The name is historical. The core has been digital since the introduction of time-division multiplexing, and most long-haul transport is now IP, but the abstraction the network presents is unchanged: dial a number in a global numbering plan and reach the endpoint assigned to it, regardless of which of thousands of interconnected carriers serves either end.
The audio constraint is the one that shapes voice AI most. Traditional PSTN voice is sampled at 8 kHz and encoded with G.711 or a lower-bitrate codec, giving a passband of roughly 300 to 3400 Hz. That was chosen for intelligibility of human speech at minimum bandwidth. It removes exactly the high-frequency energy that speech recognisers use to distinguish fricatives, which is why telephony ASR is a distinct problem from ASR generally.
Reaching the PSTN from software means going through a carrier or a CPaaS provider, which brings number provisioning, per-minute charges, interconnection agreements, emergency-calling obligations, and jurisdiction-specific rules on who may be called and when. Those obligations attach to the number and the calling party, not to the software making the call.
Related terms
SIP
SIP is the signalling protocol used to establish, modify and terminate real-time voice and video sessions over IP networks.
Carrier
A carrier is a company that operates telephone network infrastructure and terminates or originates calls on it.
DID
A DID is a telephone number assigned to an organisation that routes an inbound call directly to a specific destination without passing through an operator.
E.164
E.164 is the ITU standard that defines the international public telephone numbering plan, giving every number a unique globally routable form.