A staple of English coat construction since at least the 1850s, the Raglan sleeve, or rather shoulder, is distinctive and one of the distinguishing marks of a more casual coat.
The Raglan sleeve is more properly a way to cut the shoulder of the coat. Unlike the standard sleeve, it is not stitched to the shoulder piece or panels, but actually cut from a larger piece so that the entire sleeve construction ends at the collar. This is quite unlike the structured shoulder that we see on dress coats.
You can see the Raglan sleeve on tweed coats, raincoats, casual shirts and casual jackets (some leather jackets have them). As noted above, the Raglan is not going to give you that angular shoulder, should you want it, but rather a casual, unstructured look. In fact, you don’t really need a tailor to make one up.
Where did it come from? Not surprisingly, it is named after the man who is said to have invented, it, Lord Raglan. Famous since the 1850s for being the man who ordered the charge of the Light Brigade into Russian guns, he was in his time a much decorated and successful general, though well past his prime when the Crimean war came along.
He lost his right arm at Waterloo (where he distinguished himself to the point that he was recommended for a barony (hence the Lord, in Lord Raglan), which made it difficult to put on his uniform jacket. His tailor, who worked for Aquascutum established 1851) designed a radically new type of sleeve with a diagonal seam from armpit to collar, making it easier to wear if you had only one arm.
And the rest, as they say, is history.