After you have created a new segment, you have the options to edit or delete the segment. This will only work for segments you've created with your own data.
To find your created segments, hover over the Dashboard tab from any page on Strava and click My Segments from the drop-down menu. Then click to view the Created Segments tab.
Edit or Delete a Segment
Click on the segment in the list that you wish to edit. From the segment page, click on the Actions menu and select either Edit or Delete.