The dye is printed using a digital printer which prints the image in reverse on a dye sublimation transfer paper. Once printed, this paper is matched up to a piece or roll of polyester material (or other oil-based fabric - natural fibers like cotton and linen will not work with this print method), and fed slowly through a set of heated rollers at around 400°F. The pressure combines with the heat to turn the dye into a gas, while simultaneously opening the pores of the cells of the fabric, thus infusing the dye into the open pores.
As the fabric cools, the porous cells close, trapping the dyed colors into the cellular structure of the fabric. This is why dye sub printed materials are resistant to fading compared to other types of printing.Another feature of this type of printing is that because the dye turns gaseous, it creates a continuous tone print compared to other types of "dots per inch" printing, and is more like a photograph than a digitally printed banner or sign. This is one of the reasons
Now, back to the original question as to what commercial applications dye sublimation printing is used in. One of the biggest categories is trade shows. Booths and collateral banners and displays are often constructed from fabric which has been dye sub printed. There are polyester fabrics with some spandex-like material in them which are suited to stretching over frames.
Banner stands, which also can be used at conventions, work well with fabric banners. There are also outdoor banner stands that can be put in the ground, or weighted on the ground that are often used on the street in front of businesses such as car lots or grocery stores or pretty much any store that is trying to attract passersby inexpensively. These can go by the name of "teardrop" or "feather" or "flag" banners, as well as pop-up banners that are in the shape of a triangle that sit on the ground, although these would be more often found in an interior retail environment.
This should give you at least a partial idea of where dye sublimation printed cloth or fabric can be utilized, but the sky is the limit. Pole banners, flags, and more are useable outdoors now, and there are other items that I'm sure I'm missing off the cuff here, but you get the picture. It is the best and one of the most durable print types available, and it is, in my opinion, also the most attractive