Aram is a kingdom northeast of Israel, with its capital Damascus. It is the region of modern-day Syria.
During the reign of King David, it was conquered and paid tribute, but after the division, it became an adversary.
Later, it disappeared after being occupied by Assyria, but as the region was occupied by Assyria and Babylon, Aramaic language and script became the official languages.
The Israelites who were taken captive by them naturally learned Aramaic there, and when they were released by Persia and returned, they naturally used Aramaic.
It is the academic consensus that Jesus also used Aramaic.