The Lernaean Hydra was a serpentine water monster in Greek mythology. Its lair was the lake of Lerna, which was thought of being an entrance to the Underworld. The Hydra was supposed to be the offspring of Typhon and Echidna. Later versions of the story add a regeneration feature to the monster. In the original myth, the monster is killed by Heracles (aka Hercules) as the second of his Twelve Labors.
In D&D, the hydra is also a reptilian horror with a crocodilian body and multiple heads on long, serpentine necks. Although its heads can be severed, the hydra magically regrows them in short order. It’s far from unique, though.
Hydras lurk in swamps, bogs, and flooded caverns, preying upon virtually anything that crosses its path. They usually lurk out of sight, hoping to surprise prey. When the time is right, it slithers out of hiding and attacks with its multiple heads.
House Phiarlan, the elven dragonmarked house, uses the Hydra as a featured symbol in its crest, probably representing the artistic divisions within the house (Memory, Motion, Music, Shape and Shadow). To the public, Phiarlan is a house of entertainment comprised of bards, actors, artists and acrobats though, in secret it is a house of spies.
In your campaign
Being a very well known monster, hydras are usually not a difficult challenge to the heroes, since they are quick to burn the cut-out heads to prevent them from growing again. The best way to surprise them is having fire accelerate the process, as the hydra they’re fighting is actually an arcane-enhanced monster. I changed this vulnerability from fire to acid.
You can find the official stats for the 5e Hydra here.