The Court Wizard Calcelmo reveals that the name, Nimhe, was given to the spider by his workers, and it translates to 'The Poisoned One.' Calcelmo asks the Dragonborn to kill Nimhe since she has been interfering with his excavations for months. In exchange for killing Nimhe, Calcelmo will give the Dragonborn the keys to his Dwemer Museum and the excavation site. Nimhe appears to have killed Alethius (a bodyguard for some expeditioners who delved into Nchuand-Zel.)
An easy way to defeat Nimhe is to use destruction magic spells and attack her from the tunnel to Nimhe's lair. Nimhe cannot crawl nor attack through the small tunnel (with the exception of the poison she shoots) that you enter Nimhe's lair from, making this area a wonderful spot to attack from.
This can be a tough fight for melee characters, especially on higher difficulties. Directly across from the entrance where you first come in, an egg sac sits on the raised platform near the exit. By crouching and hiding behind it, Nimhe can't hit you with its poison attack, and can't climb the stairs, giving you lots of time to replenish stamina and magicka. It might take a while, but it definitely makes the fight a lot easier.
Nimhe can be easily killed using high sneak ability. For this, take a corner and pelt her with arrows, the result will be minimum to no damage to your character and the giant spider will be slained.
"Nimhe" (pronounced "nivah") is the Irish Gaelic adjective for 'poisonous,' coming from the noun 'nimh,' or poison. This nomenclature would be used as the cave was originally occupied by the Dwemer (Dwarves). The language of the Dwarves (in many instances of lore) is analogous to the traditional Gaelic. It is also possible that the name was given to the spider by the Goidelic (ancient Irish) inspired Reachmen working for Calcelmo.