What is a removal proceeding?

Eduardo writes, "Item number 3 of the form I-821d requires me to answer if I have ever been in a removal proceeding? I have never received an order of deportation, but I did have contact with the Border Patrol while trying to sneak through the US-Mexico border. The officers only fingerprinted me and took me back to Mexico. I sneaked back to the US in less than a week. Should I check YES or NO?"

A removal proceeding is legal action in which authorities get an order from an immigration court to remove a person from the United States who is here illegally.  This will typically involve an arrest, imprisonment, court proceeding, and then eventually deportation.  Now, legally you were not in removal proceedings (the rules for border enforcement within a 100 mile distance and on airports/seaport are different and anyone can be turned away without a legal proceeding) and can answer NO to that question.  However, in part 7 and under item 3(d) you should explain what happened when you were sent back.  Remember when they run your fingerprints through the database that record will show up in your record and the USCIS will like you to report that voluntarily.