Can I leave my luggage here?
ba-GA-gli — three syllables, stress on the second. The 'gli' is a palatal sound unique to Italian.
When you arrive before your room is ready. Almost all hotels will store luggage free of charge.
'Posso' is the first person singular of 'potere' (can/to be able to). 'Lasciare' means 'to leave behind'. 'Bagagli' is the plural of 'bagaglio' (luggage/bag). Note that Italian uses 'bagagli' where English uses the uncountable 'luggage'.
Posso ritirare i bagagli più tardi?
Can I collect my luggage later?
Ask this when leaving luggage after check-out
C'è un deposito bagagli?
Is there a luggage storage room?
Larger hotels have dedicated storage rooms
La camera non è ancora pronta?
Is the room not ready yet?
Ask gently if check-in time has passed but your room is unavailable
It is perfectly normal to check out at noon, leave your bags at the hotel, and spend the afternoon exploring before catching an evening train. Italian hotels accommodate this routinely and never charge for it.