If you believe the immigration judge made a legal or factual error, you can ask the Board of Immigration Appeals to review the decision. The Board can review decisions on removability, eligibility for relief, and bond.
There are decisions it cannot review. Credible fear and reasonable fear determinations are not appealable to the Board, and neither are claimed status review proceedings. If that is where your case ended, an appeal is the wrong instrument and something else has to be considered.
Because the Board reviews the record that already exists, the quality of what was built in front of the immigration judge largely determines what an appeal can achieve. Evidence that was never submitted below is generally not something the Board weighs — that is what a motion to reopen is for.
A decision of an immigration judge becomes final unless a party timely appeals it or the case is certified to the Board.