Post-Exile (First Exile, that is—in Babylon), Hebrew was flooded with Aramaic words and expressions, as the returning Judeans sought to introduce the sophistication of the prestigious and cosmopolitan Babylon, where they had lived for over three generations, into the provincial backwater of their ancestral land, where only poor and barely literate Judeans (“none remained, save the poorest sort of the people of the land”—II Kings 24:14) had remained after the Babylonian conquest some 75 years before.
Were it not for their glimmer of pride in the heroic Judean past (the Ten Commandments, the Judges, the kingdoms of David and Solomon, and all that), the returning exiles would have gladly replaced the Hebrew language entirely with Aramaic.
As it is, they chose only to replace the ancestral Hebrew script with the Aramaic one, on the grounds that the ancestral script was ktav libonaah (“a <something> script”—the meaning of which is unclear, but it sounds pejorative), adopted Aramaic in entire passages of certain books in the biblical canon (Daniel and Ezra), and of course in the Talmud.
That heavy Aramaic influence continues to this day.
For a good summary of this topic, see History of the Hebrew Language by David Steinberg