As Zacs says, storing files 'in the cloud' just means storing them on remote servers (= computers) that you connect to via the internet.
Some services are free to use up to a certain amount of storage space but you then pay for additional space. For example, Microsoft OneDrive gives you 5 GB of free storage but if you want more than that (up to 100 GB) it costs £1.99 per month. If you need even more storage (up to 1000 GB = 1 TB), you can either pay £5.99 per month or £59.99, with both of those offers also getting you a Microsoft 365 account:
https://www.microsoft.com/en-gb/microsoft-365/onedrive/online-cloud-storage
Google Drive is more generous with the amount of free storage that you get, allowing you 15 GB.
https://www.google.com/intl/en_ng/drive/
There are many other services. Although I hate recommending PC World to anyone, their own cloud storage is frequently awarded "Best Buy" in the UK technical press. There's no free storage but you get a whopping 200 GB for £20 per year or ten times that amount (2 TB) for £40 per year:
https://www.currys.co.uk/gbuk/cloud-642-commercial.html