Skype on desktop already supports screen sharing, but this is a brand new addition for the iOS and Android apps and was previously in beta testing earlier this year. To find the feature on your iPhone, start a Skype call, tap the "..." menu at the bottom right of the screen, and choose to start sharing your screen.
The company has also redesigned the app to streamline video calls: users can simply tap to dismiss all call controls so they can see their friend or family member without any obstructions. To remove all UI from the call, they can double tap the screen, and then single tap again to bring everything back.
Skype for iPhone is available to download for free [Direct Link], and the new screen sharing feature is available on devices running iOS 12 and up.