Spiders have a protective exoskeleton that they have to shed periodically throughout their lives as they grow. Another way of putting it is that they shed their skin as they grow larger. This process is generally called moulting, although it has a more scientific term, ecdysis. The exoskeleton underneath is soft and so once the spider is free of its old skin, it has to wait for the newly exposed one to harden.
I have never actually witnessed this process of a spider shedding an exoskeleton, but found evidence of it outside my kitchen door yesterday morning. The images are not particularly good – the wind was tossing this remnant about – yet I find it interesting to see how the spider used a length of thread to anchor itself to the metal bar above it before starting the process of emerging from its ‘skin’.