When shopping for a web host, the amount of "Storage" or "Disk Space" that they advertise refers to the amount of room that you are allow to use on their web servers hard drive to store your files. This will usually be measured in gigabytes (GB). Many of todays top web hosting companies will offer "Unlimited Storage" with your hosting plans.
Since there is really no such thing as an "Unlimited" sized hard drive, what this actually means is that they do not impose a limit in how much stuff you can store in your hosting folder. However they will point out in their disclaimer that there are limits imposed by the finite amount of the actual storage size of the drive.
The amount of storage that you are allowed is more of a flashy sells technique than actual value in most cases. Most html files are relatively small. Large sites with thousands of pages rarely exceed 1 GB. You can however use up a lot of disk space if you will be hosting videos or other multi-media format files. Consider your needs and other factors when determining which web hosting provider to do business with.