If you have a large external disk drive that you have formatted under a recent version of Windows you may find it has been formatted as NTFS. This is a Microsoft proprietary file system that Apple do not support write access to. So you will be able to read from but not write to this drive on your Mac. The older filesystem FAT32 (that did read and write on both systems) is now discouraged and newer versions of Windows do not offer this as a formatting option.
If you want to use the drive on both Mac and Windows you could reformat it as exFAT, which both support fully or you have to load a software driver on the Mac to let you write to these file systems.
I found this article (http://www.howtogeek.com/236055/how-to-write-to-ntfs-drives-on-a-mac/) that has three important points in it:
1) Windows does let you format drives with exFAT, which is the best solution since both Mac and Windows can read/write them. Obviously formatting will remove any data on the drive.
2) Users with Seagate drives can download a free copy of Paragon NTFS driver for Mac from here (http://www.seagate.com/support/downloads/item/ntfs-driver-for-mac-os-master-dl/), but I think this probably only works for Seagate drives.
3) There is still a way to get the free driver installed, and it is described in the article. It is a bit tortuous but I managed to do it on my Mac and it works fine.