Q: How to transfer my files from macbook air to WD external hard drive?

check your permissions for that macbook

What are permissions?

Every file and folder on a Mac OS X hard drive has a set of permissions —settings that determine which user(s) have access to each item, and exactly what that access is. For example, permissions dictate whether or not a particular user can open and edit a particular file. But permissions also determine which items the operating system—or specific parts of it—can access and modify, and which files are accessible by applications.

http://support.apple.com/kb/HT2963

If that fails:

offload all data from the WD to a safe place.

format the WD in disk utility as MAC OSX extended journaled

All WD drives, alas, should be wiped clean of their resident spamware 'applications'

I can think of two possible issues, the first being that you need to force the drive to ignore ownership. This has to do with the permissions that PV refers to in his response above.

After connecting the external drive to your computer:

1. Select the disk and choose File > Get Info.
2. Click the disclosure triangle next to Sharing & Permissions to expand that section.
3. Select the “Ignore ownership on this volume” checkbox.

The second possibility is that you've bought a hard drive that is preformatted for Windows in the NTFS format which Macs can read but not write to. You can verify this by launching Disk Utility (it is a program in your Utilities folder), select the drive in the lefthand column and then look at the bottom of the display for Partition Map Scheme. It should read GUID partition table. If it does not you have two solutions, reformat it or install a 3rd party NTFS driver. The linked program is the one that most agree is the most reliable and stable.