Leviathan is the sea-monster who most famously shows up in the book of Job—ruler "over all the Children of Pride." But here he reappears again as a power that (like in Job) represents the various oppressions foisted on humanity. Yet, unlike in Job, Leviathan is a power that will eventually be defeated:
On that day the Lord with his cruel and great and strong sword will punish Leviathan the fleeing serpent, Leviathan the twisting serpent, and he will kill the dragon that is in the sea. (Isaiah 27:1)
(This is a one-God-version of a story that also exists in Babylonian myth: the high god, Marduk, defeats the evil sea-dragon, Tiamat.)
Here, the dragon is also called "Rahab"—a name reserved to describe the nation of Egypt as another incarnation of the ferocious sea-serpent (Isaiah 51:9). (To avoid confusion: there is also a woman who helps the Israelite's bring down Jericho, who is also named Rahab.) The name itself just means "broad or "large," while Leviathan means "twisted" or "coiled." Keeping these meanings in mind, it's easy to see how Leviathan-Rahab together symbolize the power of oppression that is massed against Israel, whether those are outside forces like Egypt, Assyria, and Babylon, or the country's own propensity towards wickedness or forgetfulness.
In Job, God doesn't promise to relieve the suffering of human beings living under the power of the Leviathan (or, as Herman Melville interpreted the myth in Moby Dick, suffering under the Law of Nature itself). Although Job himself does escape suffering, at the end. But in Isaiah, God is promising to defeat this power at the end of time, liberating people once and for all from the crushing power of the Leviathan. (In fact, there's a tradition in Jewish folklore that imagines the surviving remnant of the righteous people of Israel holding a massive banquet where they feast on the corpse of the Leviathan at the end of the world.)