The Spider chasing the Boy in the Forest.

The Spider is a creature mainly encountered during the Forest section of the game and is considered the main antagonist of the story. Representing a giant arachnid, the creature continually follows the Boy throughout the Forest. It is an opportunistic killer, impaling the boy whenever one of its eight legs is within range. The Spider's motives for attempting to kill the boy are unknown; some argue that the spider is simply hungry, or that the Spider represents Death (or the Grim Reaper). One particular theory states that when the Boy was alive, he suffered from arachnophobia (the fear of spiders.) The arachnid could be the manifestation of his fear.

When the boy first meets the Spider, it tries impaling him, but the Boy uses a beartrap to cut off three of its legs. Enraged, the Spider goes on a rampage throughout the forest, killing other children in order to get to him. After evading the arachnid through great chasms and small caves, he releases a boulder onto it which knocks the spider into a small hole. Later on, the spider is seen for the final time, with a single leg. The Boy then tears the one leg off after dodging an attack, and uses the body as a bridge to get across a chasm.

The spider appears to be notorious in the world of Limbo, and the other children hide from it and fear it. They set traps and other defenses to protect themselves from it. They even try to imitate it by building a machine similiar to its impaling legs. 

There is a Glitch that can occur when the spider has one leg left. When the leg is about to stab the boy, the boy can run under the leg and not be stabbed. However, this causes the boy to be knocked onto his back and die. For a strange reason, the boy dies whenever he falls on his back or face, except for when it is supposed to, such as when he falls down a hill from escaping the spider.  

The spider is also a missing link in the theory that Limbo is INSIDE’s prequel. In INSIDE there are many hints to Limbo, but no spider. It could represent death...