The cloud can give you access to hardware, software and infrastructure that would be prohibitively expensive for a person or company to purchase outright. But what you are able to do with it depends upon how much you are willing to pay for the privilege.
While there are lots of free cloud options for individual users -- quite useful for things like e-mail and document and photo storage -- most of them start to charge you monthly or annual fees when you want to store more than a few gigabytes' worth of data. You could easily hit your limit right in the middle of transferring the 100 or so pictures you took of your children, pets and meals this week. Of course, the error message saying you have run out of space is likely to be accompanied by instructions on how you can purchase more.
Cloud services geared toward businesses offer a lot more space and capability, with various types and levels of service. Companies can pay for things like per-gigabyte storage or database space, rental for dedicated servers (physical, virtual or both) with varying amounts of memory and storage on an hourly or monthly basis, hosted software applications on a per-user basis, network bandwidth usage, additional IP addresses and IT management services. The ability to ramp up service quickly and pay only for what you use or think you will use are big advantages. However, if you underestimate your needs and don't opt for enough space or enough servers, you could run into issues while working with your data. Hitting a storage wall is a lot worse when you are uploading time-sensitive customer data than when you are saving your dog photos.
Still, if you're willing to pay for it, you can always add more. And some cloud setups will scale automatically as your usage changes. (Although this might result in sticker shock when you get the monthly bill.)