It depends mainly if your itinerary requires API (Advanced Passenger Information); and if so, you generally provide this at the airline's website - as they are ultimately responsible for forwarding this information to the relevant authorities.
API is required for most international travel (at least, mainly if you are traveling to Europe or the US) for some Asian countries its a hit and miss.
If you are going to be using any sort of express check-in service (like a baggage drop and online checkin) it is always better to provide this information.
If you plug in your reservation code and your last name at the airline website's "retrieve booking" function, you'll find out if you need to provide these details or not.
If you are a frequent flier with the airline, they generally keep your passport information linked with your FF number to make bookings a lot easier, so make sure once you have booked with Expedia that you update the reservation with the airline and add your FF numbers. For most airlines, doing so will automatically update your passport information on the reservation.