You have the option to delete a segment or to delete all profiles within a segment.

Delete a segment
To delete a segment, click on Audience > Segments.  Select "Delete" from the triple-dot menu on the right.  This action will delete your segment name and criteria but will not delete the profiles from that segment from your account.

Alternatively, you can delete a segment by clicking on the segment, then click on the arrow menu next to the segment name. From the drop-down menu, you can click on Delete Segment to delete the segment.

Delete an Audience
To delete an existing Audience, first select the Audience you want to delete. Once in your Audience, you can click the arrow menu on the top of your screen. 

From the drop-down, you can choose to 'Delete All Profiles' or 'Delete Segment.' 

Delete All Profiles: this will delete the profiles in your Audience from your account but keep the Audience name and criteria. 

Delete Segment:  this action will delete ALL profiles in your Audience AND the segment/list from your list view.

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