The word has become synonymous with any large sea monster or creature. In literature (e.g., Herman Melville's Moby-Dick) it refers to great whales, and in Modern Hebrew, it means simply "whale." It is described extensively in Job 41 and mentioned in Isaiah 27:1.
In Psalm 74 God is said to "break the heads of Leviathan in pieces" before giving his flesh to the people of the wilderness; in Psalm 104 God is praised for having made all things, including Leviathan; and in Isaiah 27:1 he is called the "wriggling serpent" who will be killed at the end of time.
Later Jewish sources describe Leviathan as a dragon who lives over the Sources of the Deep and who, along with the male land-monster Behemoth, will be served up to the righteous at the end of time.
When the Jewish midrash (explanations of the Bible) were being composed, it was held that God originally produced a male and a female leviathan, but lest in multiplying the species should destroy the world, he slew the female, reserving her flesh for the banquet that will be given to the righteous on the advent of the Messiah (B. B. 74b).
Rashi's commentary on Genesis 1:21 repeats the tradition: "God created the great sea monsters - taninim. According to legend this refers to the Leviathan and its mate. God created a male and female Leviathan, then killed the female and salted it for the righteous, for if the Leviathans were to procreate the world could not stand before them." 
In the Talmud Baba Bathra 74b it is told that the Leviathan will be slain and its flesh served as a feast to the righteous in [the] Time to Come, and its skin used to cover the tent where the banquet will take place. The festival of Sukkot (Festival of Booths) therefore concludes with a prayer recited upon leaving the sukkah (booth): "May it be your will, Lord our God and God of our forefathers, that just as I have fulfilled and dwelt in this sukkah, so may I merit in the coming year to dwell in the sukkah of the skin of Leviathan. Next year in Jerusalem." 
The enormous size of the Leviathan is described by Johanan bar Nappaha, from whom proceeded nearly all the aggadot concerning this monster: "Once we went in a ship and saw a fish which put his head out of the water. He had horns upon which was written: 'I am one of the meanest creatures that inhabit the sea. I am three hundred miles in length, and enter this day into the jaws of the Leviathan'" (B. B. l.c.).
When the Leviathan is hungry, reports Rabbi Dimi in the name of Rabbi Johanan, he sends forth from his mouth a heat so great as to make all the waters of the deep boil, and if he would put his head into Paradise no living creature could endure the odor of him (ib.). His abode is the Mediterranean Sea; and the waters of the Jordan fall into his mouth (Bek. 55b; B. B. l.c.).
In a legend recorded in the Midrash called Pirke de-Rabbi Eliezer it is stated that the fish which swallowed Jonah narrowly avoided being eaten by the Leviathan, which eats one whale each day.
The body of the Leviathan, especially his eyes, possesses great illuminating power. This was the opinion of Rabbi Eliezer, who, in the course of a voyage in company with Rabbi Joshua, explained to the latter, when frightened by the sudden appearance of a brilliant light, that it probably proceeded from the eyes of the Leviathan. He referred his companion to the words of Job xli. 18: "By his neesings a light doth shine, and his eyes are like the eyelids of the morning" (B. B. l.c.). However, in spite of his supernatural strength, the leviathan is afraid of a small worm called "kilbit", which clings to the gills of large fish and kills them (Shab. 77b).
In the eleventh century piyyut (religious poem), Akdamut, recited on Shavuot (Pentecost), it is envisioned that, ultimately, God will slaughter the Leviathan, which is described as having "mighty fins" (and, therefore, a kosher fish, not an inedible snake or crocodile), and it will be served as a sumptuous banquet for all the righteous in Heaven.