Does the premium version of Microsoft 365 really give you extra space on your laptop?

No, it means it gives you 6TB of space on Microsoft’s servers, should you decide to save your documents online.
It is not possible to just “create” disk space on your laptop, just as it is not possible to “download more ram”.

As loli pointed out, it’s cloud storage not physical hard drive storage on your computer

All correct above. That is available storage space using MS OneDrive, an online (cloud) storage platform. It’s great for accessing your files from any computer and collaborating with others — if you’re okay with storing your stuff on Microsoft’s servers.

I’ve been using Office 365 for 5 years. My laptop has very limited storage, but I’ve never run out of space on it, because everything is saved to Microsoft servers (the cloud). I love it, because I can access my files from any device with internet access. I do not know if I have premium. I pay $100/year for a family plan, and my children get free use of the Office apps and storage.

Agreed with all of the above. But the fact that @Nevada83 had to ask means that Microsoft’s advertising is both effective and deceptive.

For $100 I purchased a 5TB external hard drive that I can take anywhere I need to go. I’ve survived 20 years without instant access to all my files plus my getting instant access also means every hacker can get instant access whenever they discover that my door is open. Keeping my important files on the external also means that they aren’t available to be hacked while I sleep as I disconnect it before going to bed

One thing that should be considered is that if you use cloud service like OneDrive then Microsoft are providing a greater level of protection against lost files and equipment failure than if you just have everything on HD at home. Hard drives can and do fail so you should be backing up regularly to at least a second HD (or more depending on how paranoid you are). Onedrive offers an extra layer of redundancy and if you have your home PC syncing with onedrive its even possible to recover files that have been deleted from the recycle bin relatively easily.

Microsoft also retains the rights to your files IF &/or when you pass on. I’d rather buy 2 HD’s & keep my backups on site!!! How long before hackers start hacking into OneDrive??? My guess is that they have already & Microsoft just isn’t telling us. Yes, I’m a member of the ultra paranoid group!!!