For whatever it's worth ObamaCare is not a type of insurance or some specific plan. People seem to be in the habit of referring to individual policies sold through one of the state or federal exchanges as an ObamaCare policy. Healthcare reform set certain minimum benefits that must be present in all health insurance policies with some exceptions granted to grandfathered plans.
As part of a "shared responsibility" requirement all (with some narrow exceptions) citizens are required to maintain "Minimum Essential Coverage" either individually or through an employer. Failing to maintain coverage will trigger a penalty that grows every year. For 2015 the penalty is $325 for an adult or 2% of your AGI whichever is greater. In the event of coverage for a partial year you will pay a prorated penalty.
Starting this year there is a new tax form that you likely will have received indicating your coverage for each given month of the year.
1095-A: Individual coverage
1095-B: Fully insured employer plan
1095-C: Self funded & large employer plan
In the case of a large employer offering a fully insured plan you'll
receive both a 1095-B and a 1095-C.
There have been some concessions made to employers regarding these forms and as such the requirement to include a 1095-B or 1095-C with your individual taxes has been waived. If you received tax-subsidized coverage at an exchange you should include the 1095-A you received. In turbotax there was a quick checkbox to indicate that you had coverage for the year.