The term and concept of "allodial title" is largely irrelevant in current U.S. legal systems and not recognized as valid type of title. Allodial title is not marketable title and generally is unrecognized in most state courts.
As a historical concept, in a state of nature, "allodial title" describes complete, unfettered and unencumbered ownership of land for those that possessed, occupied, and held land by force against all others: there was no previous owner of allodial land, nor any superior rights, so force alone established ownership in the power vaccuum.
So the concept of "allodial title" refers to land that is held by force, without encumbrance from any superior interest or landord. Consequently "allodial titles" cannot be mortgaged, because superior interests are not valid agaist such title.
At this point, it generally only applies to sovereign governments that have ultimate right to possession -- depending on the government involved. Several U.S. states mention the term in their constitutions, to distinguish the state's origins free from feudal encumbrances inapplicable to the original 13 colonies and later states.
More recently, it was embraced as a concept in Texas and Nevada, as a means to mitigate onerous property taxes or zoning restriction on rural landowners who suddenly found their property part of a municipal corporation with new, corresponding tax burdens; such allodial titles exempted property owners from the additional property tax burden.
Nevada ceased accepting applications for allodial title in 2006.