Section 212(h) of the Immigration and Nationality Act provides that the Attorney General may, in his discretion, waive the application of subparagraph 212(a)(2)(A)(I) (crimes involving moral turpitude), 212(a)(2)(B) (multiple criminal convictions), 212(a)(2)(D) (prostitution and commercial vice), 212(a)(2)(E) (certain aliens who have asserted immunity from prosecution), and 212(a)(2)(A)(i)(II) (an offense of simple possession of 30 grams or less of marijuana).
As a practical matter, most deported immigrants who may take advantage of the 212(h) waiver will do so based on having one or more convictions for a crime involving moral turpitude (CIMT), or a single conviction of possession of 30 grams or less of marijuana. For example, there are many people who were living in the United States for many years without immigration status, and then they were arrested for having a joint, or a baggie of marijuana. After they pleaded guilty, ICE took them into detention and they were either deported or accepted voluntary departure.
Other times, people were arrested for shoplifting, or a misdemeanor domestic violence offense. After pleading guilty, these people are also often taken into ICE detention, where they accept voluntary departure of deportation. These are considered to be crimes involving moral turpitude, and if someone pleads guilty to a crime involving moral turpitude--or even to possession of a little bit of marijuana--they are subject to mandatory detention once they get to a detention center (if they have no immigration status). Many times, the immigration officers, or immigration judges, won't set bonds for these people, or if they do, the bonds are so high it's impossible for their families and friends to get the money together to pay the bond in the near future.
So they make the hard decision to accept a deportation or a voluntary departure, thinking that they will "fix their papers" from outside of the country. The good news is that, for many of these people, there is hope to return to the United States, sometimes with the help of a 212(h) waiver of inadmissibility.