An ancillary administration is needed when the person who has passed away lives in another state but owns property in Florida. With all the snowbirds who have second homes in the Sunshine State, this is a common form of probate here.
Primary probates are always filed in the state where a person officially lives (that is, where they work, vote, have a driver’s license, and the like). So if someone lives in New Jersey and needs to have their estate probated, their primary probate will take place in New Jersey, even if they were at their second home in Florida when they died.
But the estate in another part of the country cannot probate their Florida property. In order to legally transfer the property (or their portion of the property, if it is held “in common” with another) to their heirs, an ancillary administration must be done in Florida.