what does the iphone Side Button do?

It’s a context-sensitive “soft” button:

Used by itself - and depending on your settings and the “mode” of your device - it can be used to (not an all-inclusive list):

Turn “on” the device

Lock the device

Begin ApplePay Authentication

Initiate Guided Access

Activate SOS.

See other possibilites here:

iPhone User Guide – Apple Support (AU)

See the Sleep, Restart, and Siri sections of Use the side, Home, and other buttons on your iPhone - Apple Support

Also see the Pay with your Phone section of Make purchases using Apple Pay - Apple Support

It is also used to confirm a purchase in the App Store.