1. Please sign out of iMessage on all your devices and sign back in. If you've enabled two-step verification for the Apple ID that you use with iMessage, you must generate an application-specific password and enter it when prompted. Test.
2. Take this step if you have an iPhone linked to the same Apple ID as the Mac, and iMessage is working on the phone.
Follow the instructions in this support article, under the heading
To use Continuity for SMS and MMS with your iPhone and your Mac, iPad or iPod touch
If text forwarding is already enabled on the phone, disable it and then re-enable it.
Quit and relaunch Messages on the Mac.
Credit for this observation to ASC member Apple Advocate.
3. If you have no other devices, or if you do have them and iMessage doesn't work on any of them, then you (or someone else who knows your Apple ID and password) may have signed in to iMessage on a PC running OS X or on a virtual machine. In that case, the ID would be blacklisted by Apple, and only Apple could remove it from the blacklist.
Click the Support link at the top of this page to schedule a call from Apple Support. You might not be charged for the call if you select "Apple ID"—not the hardware model—as the product you're asking about.