Ancient Aram is (very generally) what we refer to today as Syria. The main capital was Damascus. However, it has been exceedingly difficult to conduct archaeological research in this region, due to political issues and a general lack of archaeological research prior to those political issues. Therefore, most of what we know about the ancient state of Aram-Damascus comes from texts uncovered in Assyria, as well as the Hebrew Bible.

Most groups in this region (Levant) spoke very similar languages. Aramaic is extremely close to ancient Hebrew and Phoenician, sharing the same root words and only differing in a few aspects of grammar and spelling, and of course script. All the languages are closely related, meaning that if you know one of them, it is relatively easy to figure out the others.

Where do the Arameans come from? We don't know exactly, because we haven't been able to excavate, but we can investigate parallels of nearby cultures that we have been able to excavate.

The different groups (Edomites, Arameans, Canaanites, Phoenicians, etc) are generally descended from older groups in that same area, and a political/social reorganization led to a city-state or larger political entity arising. So as for where they came from, we don't have much archaeological evidence (because we haven't been able to dig there very much), but we can use similar groups in the same general area to form a hypothetical pattern. In Canaan, semi-nomadic people settled down and created sets of city-states (which are reflected in the Amarna letters). The Edomites grew out of a subset of these Canaanites in the southeast of the Jordan and Sea of Galilee. The Moabites grew out of a subset of peoples living in western Jordan. The inhabitants of Mari (northwest Mesopotamia east of Aram-Damascus) grew out of a subset of semi-nomadic peoples who settled down and developed a city-state.

Based on these parallels, we can make an argument that something similar took place in Aram, with an indigenous group of Semitic people, perhaps semi-nomadic peoples related to the Sim'alites (nomadic pastoralists in the Mari area who lived in the north of the area) or Yaminites (the same, but to the south).

Where did they go?

Aram was conquered by the Assyrians in 732 BC, which we have recorded in Assyrian annals. That was pretty much the end of it as an autonomous group, until late in the Roman period. The Assyrians were known for displacing the peoples they conquered, and moving them to other regions and moving other peoples in. This also happened to the Israelites in 722 BC. Tiglath-Pileser III records this act in one of his inscriptions, and it is also recorded in the Bible in 2 Kings 16:9. The new group who arose after this almost certainly retained the language and the name, but was very different in terms of ethnic makeup, and were subjects to the Assyrians, the Babylonians, and the Achaemenid empires, and so on through the Roman periods, occasionally starting up kingdoms including Palmyra. Ethnically, much of Syria and southern Asia Minor is probably descended from Arameans.

Now that we have addressed the beginning and end of the Arameans, why were they so prominent?

Aram sat on the prime trade route between the three main empires of the Iron Age and later. They were situated in the perfect place to capitalize on trade between Egypt, the Mesopotamian empires, and the Hittites in Anatolia. There was a main international highway that went through Damascus. Therefore, the Arameans as a people group had many influential international economic dealings with the other ancient empires of the time. Aramaic became eventually a lingua franca through the region, a trade language that often supplanted other local languages. Because all the disparate cultures had to deal with Aramean traders, they learned to speak Aramaic, and the language flourished. Of course, this prime economic position meant that Aram was under significant military duress at many times during its existence, being conquered time and again. Most of the reason Egyptian armies campaigned through ancient Israel and Judah was to reach Aram and conquer it for its trade power.

Due to the fact that Arameans were deported throughout the Assyrian empire, and Aramaic was such an influential trade language, it is not at all surprising to see Aramaic loan words crop up in Mesopotamia.

Also, after Israel and Judah were conquered in 722 and 586 BC respectively, Hebrew began a decline in use, as the native speakers of that language were deported and Aramaic speakers moved in to replace them. Aramaic became the common language of the Levant region, and Hebrew was localized.

In fact Aramaic was the official language used by the Jewish Hasmonean rulers of Judea in the intertestamental period (142-37 BC). Therefore, it was spoken fluently by most people in that region during Jesus' lifetime. Hebrew was perhaps not spoken as much as Aramaic, and was confined to religion, where the Scriptures were written in Hebrew. But official documents and common conversation was usually in Aramaic.

As I said before, the two languages are extremely similar, much like Brazilian Portuguese and European Portuguese, perhaps even more similar. If you can read Biblical Hebrew, you can read Aramaic.

If you have any questions, please let me know and I will try to clarify or answer them.

Some sources:

James B. Pritchard, ed., Ancient Near Eastern Texts Relating to the Old Testament (3rd ed.; Princeton NJ: Princeton University Press, 1955)

Suzanne Richard (2003). Near Eastern Archaeology: A Reader (Hardcover ed.). Eisenbrauns

Lester L. Grabbe, Ancient Israel: What Do We Know and How Do We Know It? (New York: T&T Clark, 2007)