Technically speaking a keyword cannot be deleted, but a campaign (and any keywords inside that campaign) can be deleted. This means that you can move your keyword off to a new "dummy" campaign named DELETE ME, so that you can later go and delete the entire campaign.

To delete your keyword, go to the Setup Keyword page for that particular keyword. On this page, you will see the blue "Add New" button for campaigns, click this and give it a title that indicates to you that you want to delete this campaign later. Once you give it a recognizable name, scroll down to the bottom of the page and click "Save".

Now that you've moved the keyword to a new campaign, it's time to delete the campaign.

Deleting Campaigns

You can delete campaigns that you aren't using or if need to delete a keyword. On the list of campaigns (found in Reporting, then Campaigns) you should see the trash can icon on the right and you can click on it to delete any campaign.