The Kerith Ravine is home to a river somewhere east of the Jordan, which marked the eastern border of the land given to Israel. On a purely physical level, it functions (unlike the Jordan) as a place far away and hidden from King Ahab who was seeking Elijah's life because of the drought. The name Kerith means a "cutting" or "separation." While having to do with the physical nature of the river itself - as seen in the photos Jon Ericson provided - it also points to the "cutting off" of Elijah the Tishbite from Ahab and the rest of Israel who at this time are going after idols.
The language of "cutting off" is continued in 18:4-5. While Jezebel is "cutting off" the prophets in the land, Ahab has Obadiah to try find pasture to save the animals from having to be "cut off." Symbolically, then, Elijah is killed, which is likely echoed in his being fed by ravens, who are known for eating carrion.
(Ravens were known to not even feed their own young (cf. Job 38:41, Psalm 147:9), so it is a serious indictment on Ahab and Jezebel that not only do they care more about the lives of animals than the lives of the prophets, but even the unclean ravens who neglect their own young care more for God's prophet. This indictment is then transposed in the second half of the chapter as now not unclean ravens, but unclean gentiles are the ones to care for Elijah.)
Elijah, however, does not remain "cut off." Just as after the widow's son is revived after Elijah stretches out on him three times, so after three years, Elijah returns from the ravine to confront Ahab and defeat Baal.
All of this is a mockery of Baal, who as the storm god was supposed to bring rain on the earth. Of course, the drought is a direct assault on the claims of Baal, but so is the death and resurrection theme. According to House (NAC), it was explained that the reason Baal did not always bring rain on the earth was because Mot, the god of death, would kill him every year and then his sister Anat would eventually take revenge on Mot and free Baal from death. Instead, it is shown that Yahweh is the one who has control over rain and life and death.
Beyond being a symbol of death, the ravine is also a symbol of the wilderness. The author of Kings draws a number of parallels throughout the book between Elijah and Moses who was before him. Both appear before a wicked ruler. Both flee for their life. Both fast for forty days and forty nights. Both experience wind, earthquake, and fire up on a mountain. Both prepare an altar consumed by God's fire from heaven. Etc...
Similarly here, the notion of drinking from the brook and being miraculously fed with bread and meat while in the land east of the Jordan reminds us of Moses and Israel in the wilderness being fed with bread and quail from heaven. This is why it is not the Jordan itself that Elijah drinks from; rather he is east of the Jordan, outside of the land, in order to show that Elijah is a new Moses and Ahab a new Pharaoh.