The giant spider that attacks Frodo in Mordor in J.R.R. Tolkien’s legendarium is Shelob.
Shelob appears in The Two Towers, where she inhabits a tunnel near Cirith Ungol, the pass leading toward Mordor. Gollum guides Frodo and Sam into her lair, intending that Shelob will kill them so he can recover the Ring. She bites Frodo and paralyses him with her venom, but Sam uses Sting and the Phial of Galadriel to drive her away.
Shelob is not simply an oversized ordinary spider. Tolkien describes her as a descendant of Ungoliant, a primordial spider-like being from the First Age. Ungoliant helped Melkor destroy the Two Trees of Valinor before fleeing into darkness, and Shelob represents a later continuation of that monstrous lineage. A common mix-up is to identify Ungoliant as the spider in Frodo’s Mordor episode; Ungoliant belongs to the earlier mythology, while Shelob is the creature encountered by Frodo and Sam.