A T-shirt is a shirt with short sleeves, a round neck, put on over the head, without pockets. It was originally used as undershirt. This is still done, but it is also often worn as the only clothing on the upper part of the body (except that women often wear a bra under it).
The length varies, but it typically reaches the waist. One fashion is an "oversized" T-shirt, a more recent trend are tight and short T-shirts for women that frequently show part of the lower abdomen with the belly button. Often a text and/or picture is printed on it: a slogan, something funny, about an event.
The idea of the T-shirt came to the USA during WWI when US soldiers noticed the light cotton undershirts European soldiers were using while the US soldiers sweated in their wool uniforms. Since they were so much more comfortable they quickly became popular among the Americans, and because of their design they got the name T-shirt.
During WWII the T-shirt had become standard issue underwear in both the US army and navy. After WWII the T-shirt started appearing without a shirt covering it. John Wayne, Marlon Brando and James Dean all wore them on national TV. At first the public was shocked but by 1955 it had became acceptable. The T-shirt became cool when James Dean wore it in the film Rebel Without A Cause.
In the 1960s people started to tie dye and screenprint the basic T-shirt and variants such as the tank top, muscle shirt, scoop neck, V-neck etc. became popular.