Acoustic echo cancellation
What stops the other caller's voice from leaving your loudspeaker, entering your microphone and returning to them as an echo half a second later.
The algorithm knows exactly what is being sent to the speaker. An adaptive filter, classically NLMS, learns the path from speaker through the room to the microphone — effectively the room's impulse response — and subtracts the predicted echo from the mic signal. The principle dates back to Bell Labs' echo cancellers for long-distance lines in the 1960s; the acoustic version is harder because the room changes every time someone shifts in their chair.
The tricky part is double-talk, when both sides speak at once and the filter must not adapt to the local voice. Cheap loudspeakers add non-linear distortion that no linear filter can capture, so a post-processing suppressor mops up the rest. WebRTC made a capable canceller free in every browser, which is the reason laptop video calls work without a headset at all.