American Plan or AP means that apart from room rent, quoted hotel tariff includes all 3 meals as well i.e. Breakfast, Lunch & Dinner. In Europe and some other countries the American Plan is also referred to as Full Pension or Full Board Plan. This plan is good for tourists visiting remote places where availability of food outside/nearby or hygiene could be an issue.
Modified American Plan or MAP means quoted rates include two meals a day, namely breakfast and either lunch or dinner. In Europe and some other countries the Modified American Plan is also referred to as Half Pension or Half Board Plan. Preferred by most of the tourists as you can leave hotel with a good breakfast, spend the day out, have lunch at some nice local restaurant and go for dinner in the hotel after a shower.
Under Continental or CP Meal Plan, room rent and complimentary free breakfast are included in the tariff. And in case you decide to have dinner and lunch at the hotel, you always have the option to pay extra. Continental Plan is supposed to include a continental breakfast. However, hotel nowadays use the term for any kind of breakfast. Most of the hotels have breakfast buffet (for all meal plans) with tea, coffee, milk, juices, eggs, pancakes, local dishes, breads and corn flakes.
European Plan or EP will mostly have the lowest tariff in a rate card simply because it includes only room rent and no meals. This gives you the option of trying local food and save some money as well. You always have the option of paying and having food in the hotel. Another advantage of EP is that since almost every hotel has more than 1 restaurant, you are free to try and choose the one you like.