Asking Alexa to do something results in a vocal response (unless she's lost her voice), but that's not always really necessary and Amazon is experimenting with replacing Alexa's voice with other sounds to convey a response.
As The Verge reports, the change in Alexa's behavior was first discussed on Reddit. One user explained that, after asking Alexa to turn on the lights, she gave the usual "OK" response, but went on to say it would be the last time she would. In future, a beep sound would replace the "OK."
It's this switch to non-speech responses that Amazon is calling Brief Mode. Apparently, it's already rolling out to Alexa devices and will appear in the settings menu of the Alexa app. Based on the Reddit user's experience, it looks as though Brief Mode will be turned on by default so it's up to the user to disable it if they prefer speech all the time.
Beeps can't replace all responses, but any simple confirmation a command has been received will likely become a beep in Brief Mode. I would also hope Amazon expands the options to allow you to select from a range of beep sounds to act as confirmation.
If it proves successful, Brief Mode could easily expand to include multiple beep responses based on context. It may also limit how often Alexa laughs at you.