Was that USB thumb drive used on a PC and formatted by it before?
If so, it is probably formatted in NTFS which a Mac cannot write to. You'd need to go into disk utility and format it as FAT32 or ExFat for it to be usable on both windows and OS X.
Be aware that formatting a drive erases all the data on it, so it's a good idea you copy over what's on there to your computer before doing this.