"Corned" beef refers to beef cured in barrels with kernels of coarse salt--the word corn described small or granular bits.
Ironically, although beef cured in this manner was a big export from Cork, Ireland for generations, the average Irish person was unable to afford such a luxury item. The locals ate cured pork, with any luck.
After the famine, Irish people arriving in the US in the mid to late 1800's discovered that corned beef was inexpensive, and paired it with other cheap foods, in particular the cabbage and the glorious spud. Hence, corned beef and cabbage ( and spuds and carrots) is very much an Irish-American food.