As Webster 1913 alludes to in his wonderfully concise definition,
the name raglan entered fashion vocabulary after
Fitzroy James Henry Somerset, 1st Baron Raglan, had his tailor fashion a
coat which accomodated for the loss of an arm in battle.
Raglan was at first the name of the type of coat favored by Baron Raglan but in time came to refer simply to the sleeve. Such sleeves begin from the neckline of a shirt or coat via a single diagonal seam but do not do not extend the full length of the arm. This type of sewing construction allows for a wider range of motion without being too baggy.
Raglan sleeves are often a part of garments worn by those engaging in sport or exercise or who simply wish to layer lightly. Such shirts are called "baseball shirts".