Why are camera files typically prefixed "DSCN" or something similar?

Wikipedia says, DSC stands for Digital Still Camera. Would make sense then.

Your camera is a Nikon, and DSCN stands for Digital Still Capture - Nikon.

So the C is either Camera or Capture.

"Digital Still Camera - Nikon"

Most cameras follow the Design rule for Camera File systems, a specification that defines the directory structure, file format and naming pattern (among other things) of camera storage.

From the linked Wikipedia article:

The filesystem in a digital camera contains a DCIM (Digital Camera IMages) directory which can contain multiple subdirectories with names such as "123ABCDE", which consist of a unique directory number (in the range 100…999) and five alphanumeric characters, which may be freely chosen and often refer to a camera maker. These directories contain files with names such as "ABCD1234.JPG", which consist of four alphanumeric characters (often "DSC_", "DSC0" or "IMG_"), followed by a number.

As stated, manufacturers can chose to customize the first four characters of image files' names; Canon cameras, for example, prefix their files with IMG_, while Nikon cameras have the DSC_ or DSCN prefix.