I'm pretty sure that to most of you reading this article, a red shirt is just a shirt that's red. Most probably a T-shirt with or without a collar. The ones with collars might have a collar of a dark shade, while the ones without collars would have a round neck.
Err... okay, now let's not get too carried away. A red shirt is a character in a film who is destined to die shortly after being introduced. It draws it's origins from StarTrek and is probably to avoid the scenes from getting too gory for younger viewers and to get a general rating to target a larger audience.
You can read more about it at Wikipedia.