After setting up the API key for the first time, or if you returned to the website and found the error pop up stating from Google: "This page can't load Google Maps correctly" you may have to check the extra step of adding billing to your Google Project.
You can troubleshoot and setup billing with your Google API key, with this documentation:
If you are already logged into your Google account, you can also go directly to the billing area here:
When you see this error, it is typically because there is no billing information tied to your Google API Project.
If you have a small business or small blog, chance are you will never hit Googles's 100,000 monthly views thresholds for billing, but if you are interested in what they are you can check them here.