Meaning

noun (Greek mythology) monster with nine heads; when struck off each head was replaced by two new ones

noun a long faint constellation in the southern hemisphere near the equator stretching between Virgo and Cancer

noun trouble that cannot be overcome by a single effort because of its many aspects or its persistent and pervasive quality

originAfter the Hydra, from Greek mythology, which grew two new heads every time one of its heads was cut off. The biology sense alludes to the budding method of asexual reproduction that the hydra practices, similar to growing new heads. The figurative sense refers to how the creature could not be killed by a swift, decisive solution (in contrast to a Gordian knot).

Etymology from Wiktionary, CC BY-SA 3.0