A family of Microsoft word processing software products for creating web, email, and print documents.
Please ignore the nonsense posted by Jose
There are two likely causes to the problem you have stated.
First possible cause: Microsoft Word is not activated. Please check your license. Use the Menu Bar and choose Word > About Microsoft Word. In the resulting dialog it tells you the version number and license type. What does it say for you?
The second possible cause is the location of your Word documents. Mac OS allows only certain locations to be opened freely: your desktop and your Mac OS Documents folder. If your files are located elsewhere, move them to the Documents folder. A similar situation exists for documents attached to email messages. Those will always open read-only because you're not allowed to change an attachment to an email. You have to use File > Save As and save it elsewhere before you can modify a message from an email.
These are not the only two possibilities, but they are the most common for your situation.