Advantages of Warm Plates
Hot food tastes best when hot: Cold plates can rapidly cool down food, making it less tasty. This can be a particular problem when food is served buffet-style and is left to sit out for long periods of time. Warm plates keeps hot food at the right temperature.
Breakfast Foods
Breakfast food, particularly items that are made in "shifts" like toast, eggs and pancakes, needs to rest on a hot surface while the rest of the meal is prepared. Otherwise their texture will suffer. A warm plate can make a huge difference in how these foods taste.
Buffets
Buffet-style meals present the challenge of keeping food hot: The food is usually left to sit for quite awhile, and while warming trays can help reduce heat loss, heated plates will make a huge difference in your guests dining experience.
Dishwasher Platewarmer Cycles
Some dishwashers have a "plate warmer" cycle: Instead of washing dishes, the dishwasher dry heats them. Run the cycle a few minutes before you are ready to serve a meal, and your plates and serving platters will keep your food piping hot.
Other Plate Warmers
If you don't have a dishwasher, or your dishwasher doesn't offer the plate warmer cycle, there are plate warming stones (just heat them in the oven and rest your plates on them for heating) and electric plate warming pads that do the work of plate warming.