If I get this correctly, with a multi-microphone setup you can do similar background noise cancellation to what Amazon Echo does? Only it seems to remark that the audio source's position needs to be known before?
The beamforming in Pulse Audio is simply the second half of this process. Given a microphone array and a desired direction to listen in, it can control the pickup pattern of the array by delaying the signals from each mic differently.
1: I haven't really studied how Echo works, so these are mostly assumptions. 2: https://en.wikipedia.org/wiki/Beamforming