Drives must be formatted with a file system before they can be used. External drives typically come pre-formatted, often as FAT ("file allocation table", compatible with PCs and Macs) but could be NTFS. In a Mac store, you might find one formatted as HFS (also called "Mac OS Extended", not compatible with PCs) . If you were able to copy files to the drive from your PC without having to do something else first (i.e., reformat the drive), the drive came formatted as either NTFS or FAT.
Right click on the drive on your desktop and Get Info. "Format" is one of the things it will tell you. What does it say there? How about sharing and permissions at the bottom? What does it say there?