It's a permissions thing, similar to Linux. It's possible that the folder you created had admin permissions and it's asking you authenticate before you put something in there...
Incidentally, it's very rare that you'd need to reinstall the entire operating system, let alone wipe a disk.
Edit: Right click on one of the files and choose Get Info. At the bottom (Sharing & Permissions) it will tell you who the owner is and what privileges you might have (Read & Write is optimum). Then do the same on the folder you're trying to drag them into.
That said... I just noticed you're trying to copy them to an external drive. It's also possible that there could be a group ID issue on the drive, or, the drive wasn't formatted using a GUID Partition Map with a Mac OS Extended (Journaled) partition.
In short, there's a whole lot of things that could be going on here. Very hard to determine which it is without having a terminal to have a look-see.