You can access the Leave page on mobile by tapping the Menu icon in the top-left, then Leave.
The mobile Leave page shows your total holiday allowance, how much holiday you've used, and how much you have remaining. You can navigate through different leave years using the arrows near the top of the page.
You can request leave using the blue Plus button at the top of the page - just tap the button, fill in the form, and tap Request Leave.
Unfortunately the mobile leave page doesn't currently support viewing your currently booked leave. This is coming in a future update.