How can Windows 10 function on as little as 32 GB of disk space?

Windows 10 uses CompactOS, which compresses Windows files, to make them smaller:

Compact OS Compact OS installs the operating system files as compressed files. Compact OS is supported on both UEFI-based and BIOS-based devices. Unlike WIMBoot, because the files are no longer combined into a single WIM file, Windows update can replace or remove individual files as needed to help maintain the drive footprint size over time.

This can be done automatically by the Windows setup or by manually applying an Image :

DISM.EXE /Apply-Image /ImageFile:INSTALL.WIM /Index:1 /ApplyDir:C:\ /Compact:ON

or in a running Windows via this command:

COMPACT.EXE /CompactOS:always

I'm not sure what you have on your laptop but a clean Win 7 install is usually about 12GB's and Windows 10 is spec'd at 16GB's for 32 bit and 20GB's for 64 bit. All that extra on yours might be bloatware from the manufacturer. The 10 GB or so left after the Win 10 install is plenty for a 'netbook', if you want to call it, that will surf the web and word process. There are so many cloud saving options out there it is less important for data to be stored locally.

https://www.microsoft.com/en-us/windows/windows-10-specifications

Also, I would bet that these will have the Home edition and maybe a Home Starter edition like older Win 7 cheapies that won't even let you change the backround. Very small footprint on those.

Many of the Windows 8.1 devices have moved to "WIMBoot". This runs the PC from a compressed Windows image file. https://technet.microsoft.com/en-us/library/dn594399.aspx

Windows image file boot (WIMBoot) lets you set up a PC so that it runs directly from a compressed Windows image file (WIM file). WIMBoot can significantly reduce the amount of space used by Windows files. This helps you provide more free space to users, and helps you manufacture Windows on PCs with smaller drives.

Windows 10 uses compress boot which free's up 2-3GB. Windows 10 install using compress boot will only take up 7-9GB. Also there is no longer a need to make a separate partition for the recovery image which will free up an additional 4GB.

I've just done a clean install of Windows 10 and Office 365 on a 32GB HP Stream 7 and it's taking 13.9GB including about 400MB of my OneDrive files. It also supports a 32GB SD card (rumour has it that 64GB also works) which on Windows 10 can be used for personal folders and applications.

I've not forced the OS to compact using the procedure described here