The word attachment refers to the fact that the file is “attached” to the post or page you’re editing when you upload the file. If a file is uploaded directly from the Media page in the WordPress administration panel, it is not attached to any particular post or page, and is technically not an attachment. The word “attachment” is occasionally used for those uploads as well, though. Some themes list all associated attachments on posts and pages. Others display the attached images as an image gallery. Most themes don’t display the attachments associated with a post or page at all, though.
A file is detached from a post or page if that post or page is deleted. You can check if a file is attached to any particular post or page by clicking on the file in Media → Library. If it is, it will have a label called “Uploaded To” in the meta data, along with a link to the post or page it is attached to.