Each person will have their own opinions on what they believe a luxury cruise is. Some believe any cruise is a luxury, and for much of the World this is true and I will not argue that.
We on Cruising Earth try to differentiate "Luxury Cruising" by a few things like...
1) A More Personalized Service: Luxury cruises will typically have a higher crew to passenger ratio. Luxury cruises will have near a 1:1 ratio of crew members onboard to passengers. Non-luxury cruises can be upwards 1:3 or 1:4 crew members to passengers. "Personalized pampering" is what every guest can expect on a luxury cruise.
2) All Inclusive: Luxury cruises are typically all inclusive. Included round-trip airfare, included hotel near the port the night before the cruise, included transportation from the hotel to the port, free unlimited shore excursions, free unlimited beverages onboard, free pre-paid gratuities, free specialty restaurants onboard, free 24 hour room service, free Wi-Fi, free laundry service, etc. If it is available on the ship it is typically free/included in your cruise fare.
3) Gourmet Cuisine: From the food to the drinks there will be a world-class selection available onboard.
4) Spacious & Luxurious Cabins: From their size to their appointments, they will all be a step above. The bed, the linens, the lighting, the furniture, the included toiletries will all be the best. Ring for the butler and they will be there in just a moment with whatever you need.
For a "luxury cruise" you should expect to pay anywhere from $500 to $1000 per person / per day for the cruise fare.