Extreme Hardship is a legal term in the United States of America's Immigration Law.
Several waivers are available by the statute of immigration codes while some other require showing "extreme hardship" potentially caused to a qualifying family member (the US citizen or legal permanent resident's close relatives) of the defendant (person excluded from admission or being removed).
Here is a quote from BIA (Board of Immigration Appeals) rejecting appeal of a waiver: "U.S. court decisions have repeatedly held that the common results of deportation or exclusion are insufficient to prove extreme hardship.
Hassan v. INS, supra, held further that the uprooting of family and separation from friends does not necessarily amount to extreme hardship but rather represents the type of inconvenience and hardship experienced by the families of most aliens being deported.
However, their situation, if they remain in the United States, is typical to individuals separated as a result of deportation or exclusion and does not rise to the level of extreme hardship."