It means there were no social security taxes paid on your governmental wages.
When SS was started all workers were covered except employees of the railroads and state/local governments. The railroad workers are covered under a separate plan that predates social security, and state & local government workers were historically covered by state & local pension plans.
Some of the state & local government employees have been brought into social security over the past dozen years or so, but there are many that are participants in local pension plans that have nothing to do with social security. The vast majority of them will not be eligible to receive a social security old age pension, either because they never paid in any (or enough) to the program because they were participants in a pension, or because their SS old age pension is eliminated by the Windfall Elimination Provision (Social Security Online -- Information for Government Employees
The way I read the specific part of the IRS tax-tip page you are referring to is that you can take the credit if you received income from a government pension that resulted from service that was not covered by social security. Like I said at the top, it's a pension from a job in which there were no social security taxes paid on your wages.
I received the credit. I'm retired from a local government job and received regular pension payments during 2009. There were never any social security taxes withheld from my wages in that government job. In fact, my annual Social Security statement shows some small credits in the 1970's for other jobs I held before I entered government service (and some part time outside jobs I held during my first few years) and then it's nothing but a long sting of zeros up until the present. I'll never see a dime of social security money. And I never saw a dime from any of the assorted stimulus / bailouts.
This program is supposed to make up for not being eligible for any of the Making Work Pay credit, which excluded pensioners.