In the web hosting industry disk space refers to the amount of physical hard drive space a hosting company provides for their hosting plans. You are only able to store as many files as your disk space limit will allow. When searching for a web hosting provider always look for and choose a plan that allows for more storage space than you will initially require. This will leave room for growth should you need it in the future for additional sites, files or scripts.
Be extremely cautious with hosting companies who offer unlimited disk space. This is simply not possible as all hardware has physical limitations. Have you ever header of a hard drive of an unlimited size? That is exactly why you can't realistically expect the same from a web host.