The term "die cut" is used to describe the process of cutting shapes from paper and other materials. This process works a lot like a cookie cutter – we place a die cutter on our machines and run it over uncut label paper. The resulting labels have shapes cut into them that correspond to the shape of the die.
This means that the die line is the physical border of your label. You should design your label with the assumption that nothing outside the die line will print or remain on the label once it's peeled up from the liner. If you want your design to go all the way to the edges of your label (as opposed to it having a white border), consider adding a bleed.
If you're using the Custom Printed Label tool, you'll notice on the "Place Your Artwork" page of the generator that there are two borders surrounding your label. The solid "die cut" line is showing you the actual, physical border of your label. This is where the machine will be cutting. The dotted line is your bleed area.