As noted above it is probably formatted in the windows format, ntfs, and mac os x can read from that format but can not write files to it.
If you want to use it on both systems you have a couple of options.
Format it fat32 and both systems can read & write to it. That is ok except for the fat32 files size limit which is 4GB. No file can be larger than 4GBs in size (that is file size not folder size).
Format it exfat. that is a new format created by MS to get by the fat32 files size limit. The only problem with that format is the drive can get corrupted because it only has one file allocation table and if that gets corrupted all the data on the drive will be non retrievable.
Leave the format as it is and install a program on the mac that will make the mac able to write to ntfs formatted drives.
Format it in the mac format and install a program on your windows pc that can both read and write to mac formatted drives.
Leave it as it is and connected to your windows pc and network the systems across your home network. That way your mac can read and write to it along with both of your computer being able to share files without having to move the drive from one to the other.
Of course you could and should buy a second external drive for the mac so you can do time machine backups to that mac dedicated external drive.