The Medusa spider (Latrodectus regina) is a dangerous species of spider found on the Island.
Dr. Arzt showed Nikki a female Medusa spider in a jar, one of more than 20 species of insects and arachnids he had collected since crashing on the Island. He explained to her that the Medusa spider was very dangerous and that the female's pheromones were so powerful that, if the jar was opened, every male on the Island would be drawn to her in seconds. When Nikki learned that Paulo has recovered their stolen diamonds without telling her, she used the live Medusa spider specimen to attack him. After Paulo was bitten, she revealed to him that the venom of the Medusa spider wouldn't kill him, but would cause paralysis lasting for approximately 8 hours, so profound that even a doctor wouldn't be able to hear his heartbeat. ("Exposé")
Arzt's information about the pheromones was proven correct when multiple male Medusa spiders appeared in the grove following Nikki's release of the female Medusa spider from the jar. Nikki was bitten too, and both Nikki and Paulo subsequently died after being buried alive while paralyzed, having been mistaken for dead by their fellow OceanicFlight 815survivors.
Arzt refers to his Medusa spider as Latrodectus regina, which would make it a member of the widow spider genus.
"Medusa" in Greek and "regina" in Latin both translate to "queen."
The paralyzing effect of the spider's venom is likely the reason the spider is named after Medusa, a Greek creature that can turn people to stone.
The spider used in filming is Argiope appensa which is from a different genus of spiders than Latrodectus. The "males" are also females, as the real males are much smaller. Argiope appensa was introduced in Hawaii and is a very common there. It's natural range is in Taiwan and New Guinea.