When filling out Form I-90 to request a green card renewal or replacement, you must tell on the form if you were ordered removed from the United States.
In most cases, being ordered removed means that an Immigration Judge (IJ) has ordered your removal from the U.S. territory. After the judge decides to remove you from the U.S., you can still appeal to the Board of Immigration Appeals (BIA). If BIA confirms the order, then you will be deported from the U.S. and denied entering the U.S. for 5, 10, or 20 years, or even permanently.
In case you entered the U.S., and the officials of Custom and Border Protection found that you broke the immigration law, they can also remove you from the U.S. by issuing a respective order.
USCIS may reject your Form I-90 if you were ordered removed from the U.S. Note that you will also have to explain why the removal proceedings happened in your case in Part 8 on Form I-90.