If the DNA is in the cell's nucleus, the DNA will be utilized to produce whatever gene is encoded in the DNA. But if the DNA is just floating around on its own it will not survive a cell division event and the material would need to be periodically reinjected to keep working. However, if the injected DNA is part of a full chromosome, it will be replicated when the cell divides - and will be permanent as long as the cell or its progeny survive.
Some viruses will just inject the DNA into cells, but will not become part of the cell's genome ("transient" transduction). Other viruses (like lentiviruses and these adeno-associated viruses [AAVs]) inject their DNA not just into the cells, but also have machinery that splices their payload DNA directly into the cell's chromosomes ("integrated"). The location in the genome of the splicing event is relatively random. Random is not necessarily great as it could interrupt other genes already in the chromosome. CRISPR is a now-famous tool that helps "integrate" DNA into a specific spot in the genome by being guided to a specific location with a small piece of a specific sequence.
Once the DNA is integrated, any cell, and any of the cell's progeny, will produce or "express" the gene on the delivered DNA. In this case, they delivered the 5991 characters of DNA associated with the OROF gene [1].
This is actually not totally correct. AAV’s form episomes, which are circular DNA structures that are basically extra chromosomes. The fact that AAV’s don’t randomly insert themselves into DNA makes them safer for clinical uses like this.
