Short answer - anything.
There are RDP clients available for iOS - I have connected to a remote desktop with an iphone, back in the day. And on a iPad. It helps to have a bluetooth keyboard (and with an iPhone, really good eyesight).
There are also RDP clients for assorted Linux and MacOS.
The RDP protocol is pretty standard (RDP = Remote Desktop Protocol). It might be harder to connect today, I assume there is more encryption, you’ll need a VPN client or something perhaps.
Essentially what RDP does is send your keystrokes and mouse movement to the server, and relay the screen back to you so your client software can draw the screen on your device. (For iOS, your finger is the mouse. Tap to click) Depending on what options are enabled on the server, I believe you can upload/download files from local, print to a locally attached printer, connect a local thumb drive onto the remote session, etc.
So as others have pointed out, the local hardware does not have to be very advanced. It means that you can keep using your 10-year-old PC, but just as a terminal.
They do in fact sell “smart terminals” that essentially just do RDP (or the Citrix client version, or VMware’s Horizon desktop client - which are competing protocols from other virtual desktop companies). However, the electronics to do this are almost as expensive as a low end PC so why bother?
The main point is that, even if your computer is horribly infected, it cannot infect the remote virtual PC (unless you actually upload and execute the virus on the remote - and most service providers ensure their VM’s are heavily protected via AV software and locking down security. )
Windows saves your individual settings from your logon session. For virtual machines, Windows has the facility to save this “profile” data separately, on a file server. This you can logon to any different virtual desktop (or real desktop) and if it is so configured, it will fetch you userid’s profile from the server. This includes things like “Documents”, “favorites”, your email settings, recent files, etc. etc.
this means a server need only run as many VM’s as there are people logged on, instead of one for every person.
Bill gates however still wants his pound of flesh - a Windows license - for every instance of windows running, real or virtual. Did you expect anything less?