The T-shirt evolved from
undergarments used in the 19th century, through cutting the
one-piece "union suit" underwear into separate top and bottom
garments, with the top long enough to tuck under the waistband of
the bottoms. T-shirts, with and without buttons, were adopted by
miners and stevedores during the late 1800's as a convenient
covering for hot environments.
T-shirts, as a slip on garment without buttons, originally became
popular in the United States when they were issued by the U.S.
Navy during or following the Spanish American War. These were a
crew-necked, short-sleeved, white cotton undershirt to be worn
under a uniform. It became common for sailors and Marines in work
parties, the early submarines, and tropical climates to remove
their uniform "jacket," wearing (and soiling) only the undershirt.
It is possible that the Navy uniform boards first discovered the
T-shirt by watching dock crews.
Named the T-shirt due to the shape of the garment's outline, they
soon became popular as a bottom layer of clothing for workers in
various industries, including agriculture. The T-shirt was easily
fitted, easily cleaned, and inexpensive, and for this reason, it
became the shirt of choice for young boys (perhaps more the choice
of their mothers than of the boys themselves). Boy's shirts were
made in various colours and patterns, and became so ubiquitous
that cartoon character Charlie Brown rarely was seen without his
T-shirt with distinctive zig-zag stripe around the waist.
By the time of the Great Depression, the T-shirt was often the
default garment to be worn when doing farm or ranch chores, as
well as other times when modesty called for a torso covering but
conditions called for lightweight fabrics.
Following World War II it became common to see veterans wearing
their uniform trousers with their T-shirts as casual clothing, and
they became even more popular after Marlon Brando wore one in A
Streetcar Named Desire, finally achieving status as fashionable,
stand-alone, outer-wear garments.
http://en.wikipedia.org/wiki/T-shirt for more details