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Ga'agua means longing or homesickness. This talmudic word derives from the biblical ga'a, the low sound produced by cattle. The cows pulling the holy ark in the beginning of I Samuel are described as ga'u (moaning) as they went.
Midrash Tanhuma (Exodus 1) moralises on the importance of disciplining one's children. If you withhold the rod (or according to the non-violent interpretation, the rod of morality - shevet mussar), your child will take up bad ways: "That is what we find regarding Ishmael, who had ga'aguim for Abraham, who did not chastise him."
The well-known Etz Yossef commentary reads ga'gui as "longings". Ishmael always longed for his father, which caused Abraham to be lenient with him. However, Markus Jastrow, the great 19th-century talmudic lexicographer, reads ga'aguim here as sulky, rebellious conduct, recalling the moaning aspect of ga'agua: for him, the Midrash explains that although Ishmael was a sulky and rebellious child, Abraham failed to discipline him, which led to greater problems in the future.
Indeed ga'aguim are sulky feelings that try to pull us back to a different time and place. The word itself sounds like mere babble, an inarticulate cry, which is what makes it particularly beautiful.