The traditional formal shirt worn by professionals, artfully changed by uncomfortable people into an item of clothing which is actually comfortable. Generally the shirt is a white oxford, but it can be any of the traditional oxford colors, such as french blue, regular blue, pink, butter yellow, sage green, or lavender. I personally have always found pink to be noxious, but take your own preference. Tasteful stripes or contrasting white collar and cuffs are also acceptable.
A given formally dressed person would wear this shirt pressed to absolute crispness, practically implying hospital corners at the shoulder, and tucked firmly into formal slacks or skirt. This is fine and good in a formal situation, but uncomfortable and even unnecessary in most others. So I find it very nice when people wear untucked, randomly ironed shirts with jeans or shorts. This is an aesthetic as well as a sensual preference.
The shirt itself maintains its integrity while untucked, but lengthens the torso with its longer line. It can move with the wearer more freely, as opposed to being anchored at the waist. It hangs solely from the shoulder to fall over the body in a natural drape. It is less constrained in general, and thus more comfortable as well as more pleasing to the eye.
I find it worth mentioning as well that Catholic school kids risk detention on detention by having their uniform shirts untucked, yet in my high school, no one EVER tucked in their shirt until the five minute bell. No one tied their tie either. Comfort ruled until the last possible second. Why shouldn't it rule outside work in general?