Depends on the app that's requesting it. Most of the time it means that it needs access to the microphone and to record audio to then process it in the app. The processing, however, will be up to each app. Your texting app might request this for voice notes. Your keyboard app may request it for voice dictation. Bixby would request it to allow for voice commands.
As for the one from your screenshot, that's not a access request, that's different. In that, Samsung is letting you know any changes to their privacy policy and how it affects the use of your audio command snippets for system improvement (usually anonymous, personal data stripped, that might be listened to by an actual human for review); it is allowing you to opt out of this.