It is basically asking you if you have ever been convicted of a felony. As some jurisdictions call a given crime a felony while others classify it a misdemeanor, ATF has given it a generic definition of being convicted of any crime in which the maximum possible sentence exceeds 1 year in jail.
Of course, they then turn around and provide a handout on NICS with the following:
Quote:
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Currently under formal charges for a felony or convicted of a felony that can receive more than a one-year sentence or convicted of a misdemeanor that could receive more than a two year sentence.
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So basically, they are asking if you are a convicted felon. Assuming you can pass the NICS background check and own firearms, that would mean no felonys and you could answer the question as such.