I claimed 2 dependents but my refund stayed the same.

[KrisD · Accepted solution]

Claiming dependents won't always increase your refund.

Each dependent you claim gives you an exemption.

This exemption amount is subtracted from your income before your tax liability is computed. 

If your tax liability zeros out, additional dependents do not help you get a refund.

Only the refundable credits help with that, such as the Earned Income Tax Credit, the American Opportunity Credit and the Additional Child Tax Credit.