Well, the whole story began when a French priest, the Abbé Julien Gouyet of Paris, discovered a small stone building on a mountain overlooking the Aegean Sea and the ruins of ancient Ephesus in Turkey on October 18th, 1881. Abbé Julien believed it to be the house of Mary in Ephesus based on his reading of the visions of Blessed Anne Catherine Emmerich (1774-1824), but at the time, he was not taken seriously.
Ten years later, two Lazarist missionaries from Smyrna rediscovered the building - also using Emmerich’s visions as a guide. What is interesting is, they also learned that the inhabitants of a certain distant mountain village - which are purported to have descended from the Christians of Ephesus - also knew of the existence of the same ruins, which they called
Panaya Kapulu (“Chapel of the Most Holy”). These folks made an annual pilgrimage to the site during the 15th of August, the date on which most of the Christian world celebrated the Assumption, as they believed that it was the spot where Mary died and/or was assumed.
The ruins, as it stands now (as others said, the building was restored in recent times; the restored portion of the chapel is distinguished from the original remains by a line painted in red), apparently dates from the 6th-7th century AD, but parts of the foundation and some coal found on the site is taken as evidence pointing to an earlier time - probably even around the 1st century.
Now, of course the Catholic Church (Roman or Eastern or what-have-you) does not have an official position on the site, as it does on other holy places and purported relics. It is of course not required for people to believe that Mary lived here to be Catholic in good standing. It has, however, from the blessing of the first pilgrimage by Pope Leo XIII in 1896, taken a positive attitude towards the probability the house was actually the home of Mary. Pope Pius XII, in 1951, following the definition of the dogma of the Assumption in 1950, elevated the house to the status of a Holy Place, a privilege later made permanent by Pope John XXIII. Of course, such bestowals of status does not say anything about their authenticity: even if somehow it proves to be not Mary’s, it would still be a very fitting memorial to the Mother of God.
Now, I’ll admit that I have a bit of reservations about the site being the location where Mary was assumed (since virtually all of the earliest sources which mention Mary post-Jesus places the location of her tomb - and thus her Assumption - in Jerusalem, for a start), but I am willing to consider the possibility that she did live there - for a time, at least. But even if not, I personally think the site could also fit as evidence of the practice of Marian devotion among early Christians - if not her actual house, it could also be some sort of shrine the Christian community in Ephesus built in her memory and honor (perhaps even under the influence of St. John himself!)