Gage Skidmore [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
The new rule requires that migrants apply for asylum in another country before being able to apply in the United States if they crossed the border of another country on the way here. If a migrant from Guatemala who has crossed through Mexico tries to get asylum in the U.S. they need to have applied for it in Mexico and been denied before they can attempt the same here.
The rule requires that migrants apply for asylum in the first "safe" country that they come to.
In order to be considered safe, the countries will need to be a signatory on one of three international treaties: the 1951 Refugee Convention, the Protocol Relating to the Status of Refugees, or the UN Convention against Torture. If the migrant passes through countries that are not a signatory on any of the three they may still seek asylum in the United States.
Source: TTN staff