The drive is probably formatted in NTFS which is the native Windows format. Mac can read/copy from NTFS but cannot write to it.
You have to launch disk utility on the Mac to format the drive (this will erase the drive). For a Mac only format, choose Mac OS Extended (Journaled). PCs cannot see this format if you were to connect it. FAT32 will allow both Mac and PC to read/write to the drive, but individual files sizes are limited to 4GB.
