WordPress generates its pages on-the-fly, pulling information from a database. If you request a web page and the server is having a hard time talking to the database, it will sometimes display “Error establishing a database connection”.
I’ve seen this most often on less-expensive hosting accounts; almost every time it was a GoDaddy account (one reason why I rarely recommend them).
What can you do about it? Just refresh the page; often it’s only a temporary spike that goes away. If the issue remains, you may have a genuine problem and should speak to your WordPress professional.
If you’re on GoDaddy? Call their support at (480) 505-8877 and make sure your current plan is the best thing for you. You can also consider upgrading/cross-grading to one of their WordPress-specific hosting plans, often at no additional cost.