Updated: Aug 14, 2019
The Cloud as a term possibly couldn't be any more vague. To understand it in layman's terms, keep reading.
Background: Almost everyone today owns at least one mobile device - phone, tablet or another. Likewise most people have access to a computer, whether it be at home or work or both. Sharing information whether it be photos, files etc., between your different machines using cables, USB sticks etc can be messy, inconsistent and time consuming. Instead of storing information/data on individual devices/computer and connecting using cables, storing key data you wish to access from all devices in a remote, universally accessible location provides seamless access from phones, tablets or computers. That universally accessible location is the Cloud.
What is the Cloud?
The way I describe the Cloud to people who ask, is to imagine an enormous bank of big computers living and running somewhere else (probably midwest America :)) Google, Apple, Microsoft, Samsung, Dropbox - all own these huge centres of thousands of big computers. Each one of those companies offers you a small slice of memory from their computers for you to use to upload data from any of your devices to be stored and then downloaded from any other of your devices.
Free Cloud space: If you have an iPhone, Apple have automatically gifted you with 5GB of storage for free (this would save tens of thousands of emails or roughly 3 full length movies (SD)). As will Samsung, Google or Microsoft if you have accounts or devices with them, or you can simply request it. Dropbox is the main independent cloud storage provider, so not directly affiliated with any major IT vendor.
Using the Cloud: You can then use it to back up content from your phone/tablet to this online "Cloud" storage location you're given via your phone or through an Internet browser like Chrome or Safari. You can then download to your computer or vice versa. You can also purchase additional storage for extremely reasonable prices should you wish to store more content online (e.g. 50GB of storage with Apple currently costs €.99 per month).
And that's it. The Cloud = remote storage you can use to keep files and data to be easily accessed from multiple devices/machines (my definition anyway :)).
Follow my blog for a subsequent post and video showing how to download and upload files to and from the Apple iCloud. Please add any comments or questions below!