When you open your dictionary and flip to "Hydra", It would usually say something such as "A many-headed monster slain by Hercules". It doesn't really explain much about Hydra. Hydra is famous for being one of the twelve labors of Hercules.

Hydra, in greek legends, was an offspring of Typhon and Echidna. A large monster with 7 (or 9 heads. the number varies.) where the center one is immortal. When Herakles (greek for Hercules) cut a head off, two would grow in it's place. Hercules had cauterized the roots to prevent any more heads from growing as he cut them with the help of his servant Iolaus.

Now from here, I only know of two other stories. Hercules cut the immortal head and used arrows that were dipped in poisonous blood to cause serious and fatal wounds to Hydra. And the other story I know is that Hercules didn't cut the immortal head, but buried Hydra under a big rock.