As defined on the Chagiku blog, “the exclamation 아이구 'Aigu!' is used, with varying tonality, in keening for a dead parent, or expressing sympathy for another person's bad news, but it is also used on spilling a cup of coffee, or to express exasperation on just missing a bus, amazement on meeting a long-lost friend, or fury at losing one's job.

아이구 (aigoo) means something like ‘oh’ or ‘oh no’ or ‘oh my!’ It's a Korean exclamation. could also means something similar to 'geez'.”

Its use is closely related to “omo”, since both express surprise (although omo seems to have a more positive connotation).