Biblical Aramaic is the form of the Aramaic language that is used in the books of Genesis, Jeremiah, Job, Daniel, and Ezra and should not be confused with the Aramaic translations of the Tanach known as Targumim.

Hebrew is the main language of the Tanach. Aramaic only accounts for about 250 verses out of a total of over 23,000. Biblical Aramaic is closely related to Hebrew since they both are classified as langauges in the Northwest Semitic language family.

Genesis 31:47 - Witness Mount (יְגַר שָׂהֲדוּתָא) - Aramaic was Laban's language
Jeremiah 10:11 - Denunciation of idolatry
Job 36:2 - Rashi's commentary states this phrase - Wait awhile for me and I will tell you (כַּתַּר-לִי זְעֵיר, וַאֲחַוֶּךָּ) - is in Aramaic
Daniel 2:4-7:28 - Five tales about Daniel and his colleagues and an apocalyptic vision
Ezra 4:8-6:18; 7:12-26 - Correspondence about Jerusalem to Artaxerxes the king

Similarities and differences between Biblical Hebrew and Biblical Aramaic^[1]
The same square script is used.
The verb systems are based on tri-consonantal roots.
Verbal conjugations have similar functions.
Nouns have three states: absolute, construct, and emphatic.

Aramaic attaches the definite article to the end of the substantive.
The letters hey (ה) and alef (א) are interchangeable for the article.
Aramaic uses different letters to represent the same letter sounds as Hebrew.
The preposition dalet (ד) functions as a conjunction and is often used instead of the construct to indicate the genitive relationship.

Divergence of consonants between Biblical Hebrew and Biblical Aramaic^[1]

During the eighth century BCE, Aramaic became the lingua franca of the Near East.^[2] Before that period, it had been the native language of the Aramaean city-states to the east. In 701 BCE, King Hezekiah of Judah negotiated with King Sennacherib of Assyria, as his army besieged Jerusalem.

II Kings 18:26: And Eliakim the son of Hilkiah and Shebnah and Joah said to Rabshakeh, "Please speak to your servants in Aramaic for we understand it; do not speak with us in Judean within the hearing of the people who are on the wall."^[3]

The account in II Kings sets the meeting of the ambassadors of both camps just outside the city walls. Hezekiah's envoys pleaded that the Assyrians make terms in Aramaic so that the people listening could not understand. Thus, Aramaic had become the language of international dialogue, but not of the common people. In 586 BCE, King Nebuchadnezzar II of Babylon destroyed Jerusalem and exiled many of the people of Judah to the east. During the exile, Aramaic became the language of necessity for the Israelites. After the Persian Empire's capture of Babylon, it became the language of culture and learning. King Darius I declared⁴ that Aramaic was to be the official language of the western half of his empire in 500 BCE, and it is this Imperial Aramaic language that forms the basis of Biblical Aramaic.^[2]

^[1]Alger F. Johns, A Short Grammar of Biblical Aramaic. Berrien Springs, MI: Andrews University Press, 1972.
^[2]Franz Rosenthal, A Grammar of Biblical Aramaic. Wiesbaden: Otto Harrassowitz, 1961.
^[3]"The Complete Jewish Bible." chabad.org. Chabad, n.d.
^[4]Saul Shaked, "Aramaic" Encyclopedia Iranica 2. New York: Routledge & Kegan Paul, 1987.