The word panther originally signified a leopard, but nowadays has generally come to be used of black leopards. These are leopards which are melanistic. the black equivalent, as it were, of albino. However, in the United States a certain confusion has arisen, as the term panther has traditionally been used to mean a puma (Panthera concolor). The puma, to make matters even more confusing, has been known by a variety of other names: painter, mountain-lion, deer tiger, catamount, catamountain and above all, cougar.
Reports of panthers and pumas which should not normally be there have been turning up in many countries in recent decades, but I want to address the question as it applies in the United States.
In the case of pumas, when one asks where they come from, the answer is quite simple. In the first place, those states where pumas still officially exist are connected by land with those where they do not. If two dogs and a cat managed to cross the States from west to east, as chronicled in the book The Incredible Journey, it should not be impossible for some pumas to simply travel by land into areas where their species was extirpated by humans. (Discreet travel on their part would, of course, have been necessary).
In addition, some people keep pumas as pets. They may release them after a time, as they cost a lot to feed and when fully grown they look a trifle intimidating. Some may escape. These would perhaps account for a number of sightings.
Some people report sightings of "black cougars". The melanistic form of the puma is very rare. While some sources say it simply doesn't exist, there are two killings of them which seem well attested. Because of their scarcity it seems unlikely that alien big cats observed are melanistic pumas.
Large black out-of-place cats are usually described as "black panthers". It is much harder to explain how a population of genuine black panthers might get loose in the United States. However, there are other animals in Native American tradition which may be the source of the reports.
The devil-cat was the subject of Indian belief in days agone. It looked like a puma but was black and held to be a different animal. It had a tendency to carry off children and was much feared. A surviving population of these, which might for a time have existed in remote areas, may now be expanding its range. It does not sound as though this creature were a purely mythical animal.
There are also reports of a large black cat in American folklore called the wooleneag, which may be the same creature. This animal seems to have been frisking around colonial Maine. Both these creatures are mentioned in Loren Coleman's Mysterious America. It is hard to find information on the wooleneag. When I tried to locate it on a certain search engine, the reply Did you mean Woolen Bag? came up. Are that "black panthers" of America an undiscovered species?