Most content management systems will not delete files/assets when you remove them from a post/page of the website. Thus, your web server may suffer in performance as you reach your storage capacity. This is particularly true for sites that allow uploading rich media content like videos and audio files, as well several high definition/large format graphics.
In the case that you are uploading replacement files, many systems (including Drupal) do NOT OVERWRITE the previous file, but instead rename your file by adding a version number to it. If the original image was mypicture.jpg, the uploaded replacement would be called mypicture1.jpg. Keep this in mind if you replace content embedded graphics frequently, as it will eat up storage space. Site administrators typically have the ability to delete files- but should take care before deleting them, as users cannot undo the deletion.
In some CMS file managers, you may have the ability to create folders and choose where to store the uploaded files. Should that be the case, be sure to keep your folder structures/names simple and search friendly.
ONLY DELETE files you physically uploaded yourself and know are not embedded elsewhere on the website, to avoid breaking web pages that others have setup and embedded images on.