A 12:00 flasher is a person who doesn't know how to use anything but the most basic, obvious features of a gadget, never poking deeper into the options, customizing settings, or reading the instruction manual to discover the other things it can do.
It's a long-standing joke that consumer electronics tend to be lacking in the user-friendliness department. Back in the early 80s, the most high-tech thing most people owned was a VCR, and they were notoriously difficult to program. In an effort to keep costs low and internal design simple, many of the buttons on the VCR and its remote had multiple functions, and the display had only a few 7-segment LEDs to report to the user what was going on. This meant that programming the VCR required the user to navigate through multiple levels of menus with poorly-labeled buttons, following non-intuitive steps from an indecipherable instruction sheet with only a few blocky characters for feedback.
And even if you did manage to successfully so much as set the clock, it would just re-set itself the next time the power went out. Most people didn't bother, and only used their VCRs to watch movies or record programs they were currently watching, using only the clearly labeled Play, Pause, Record, Fast Foward, Rewind, and Eject buttons. This allowed them the basic functionality of the VCR but left several features unused, which pointlessly increased the price of the unit. The most visible sign of a person who didn't use any of the VCR's features was the flashing 12:00 time on the display, which indicated that the owner didn't even know how to set the clock (or, at least, didn't think it was worth the bother). Some people would go so far as to cover the display with a piece of electrical tape just to block the annoying flashing number.
Today, VCRs have on-screen programming and remotes with dozens of buttons, making them somewhat easier to set up, but the idea persists. Cell phones, mp3 players, and even the microwave oven are still limited in input buttons and user feedback, requiring most of the keys to perform multiple functions, which still makes it difficult to unlock some of their more esoteric features.
The 12:00 flasher is a special subset of computer user, as well. While many features of a personal computer are much, much easier to access and set up than they were in the mid 80s, many people either don't bother to set them, or are afraid to poke around in the guts of their expensive, delicate machine when they don't know what they're doing. With a reasonably steep learning curve to overcome and potentially catastrophic consequences for failure (real or imagined), it's understandable that many people will leave well-enough alone and simply leave all of their software in the default settings it was installed with.
The advantage to dealing with a 12:00 flasher is that, having all of the software in its default state, the interface and settings are at least familiar to anyone else who wants to use it. This is especially important for tech support purposes. The disadvantage, however, is dealing with a person who is unfamiliar with anything but the most basic and obvious features of the machine.
The existence of 12:00 flashers means that programmers and designers need to be careful how they configure the default settings, maximizing their utility for the people who won't change them while still allowing casual users to enable the more advanced features.
According to Urban Dictionary, the phrase "12:00 flasher" was popularized by the comedy troupe "Three Dead Trolls in a Baggie" in their Internet Help Desk sketch. The relevant line is "There's no way to get a 12:00 flasher on-line, okay? It cannot be done, I've seen guys eat their own headsets trying."