Krisp creates an additional layer between the physical microphone/speaker and the communicating app you are using. To remove the noise coming from other participants to you, the audio is received from the communication app, processed on your device to remove noise by Krisp Speaker, and then transmitted to your physical speakers.
To remove the noise going from you to other participants, the audio is received from your physical microphone, processed on your device to remove noise by Krisp Microphone, and then transmitted to the communication app.
For the voice cancellation, Krisp analyses your voice to start removing the significantly different voices of other people from your audio stream.
The noise/voice cancellation for the audio going to your microphone and the noise cancellation for the audio coming from your speakers is done directly on your device. The audio data is not stored anywhere or sent to any servers. Check this article to know what data Krisp sends to the cloud during its usage.