A Spider has a stiff support system on the outside of its body - called an exoskeleton, like an insect, and supports itself on its eight legs (and sometimes its abdomen). People, Mammals and other vertebrates have an inner support system and internal skeleton consisted of bones, ligaments, muscles and covered in flesh.

The exoskeleton segments of the spider are connected together with joints so the spider can move them back and forth and like people, spiders move by contracting muscles. The muscles attached on the inside of the exoskeleton contract to move the legs inward, but spiders don't have any muscles to extend the legs back out again. Instead, they have to force bodily fluids (mainly blood) into the legs to push them outward with hydraulic pressure. The exoskeleton of the spider is made up of special material called the cuticle. The composition of the cuticle is so that it makes the exoskeleton extremely strong, but it cannot expand or stretch. In order to increase its size, the spider has to form a new, larger cuticle exoskeleton and shed its old one (molting).

Here is a website that might help you understand the support system of the spider:spiders.