What does Amira mean?
Arabic 'amira', the feminine of 'amir' ('prince, commander, ruler'), meaning 'princess'. Royal but not literally 'queen' — the root a-m-r concerns command/rule. (A separate Hebrew name Amira means 'speech/treetop'.)
What does Leila mean?
Variant spelling of Layla, from Arabic 'layl' meaning 'night'. The 'Leila' form was popularized in English via 19th-century Western literature.