If you worked in both the private sector and for the federal government (and some state or local entities), then you may qualify for both Social Security benefits and a government pension.
Since Social Security benefits are disproportionately weighted towards folks with lower incomes or shorter work records, someone with a private/public work record may receive "undue" Social Security benefits.
To offset this, Social Security has a "Windfall Elimination Provision" (WEP) which can affect your Social Security benefit.
Also, if you are eligible for Social Security benefits on your spouse's record, the "Government Pension Offset" (GPO) may affect your benefit on your spouse's record.