Board basis relates to what food and drink options are included with your hotel booking.
All Inclusive means that your hotel, in addition to providing accommodation, includes a wide range of other amenities such as unlimited food, beverages, and sometimes sports activities, and daily and nightly entertainment. Golf, diving and spa services usually cost extra, as does branded drinks at some resorts.
Full Board means that breakfast, lunch and evening meals are provided, making where and when to eat each meal hassle free.
Half Board means that breakfast and another meal (usually your evening meal) will be included in the price but drinks will be chargeable. The main advantage of half board is the flexibility it provides you in the day to go and explore the local area and have lunch away from the hotel but you can also come and go as you please. In some cases you can choose to receive lunch instead of dinner - the hotel will confirm this upon arrival.
Bed and Breakfast means that breakfast is included in the price you paid for your hotel or holiday. The breakfast is normally served in a buffet style and depending on which country you're staying in there will be various breakfasts to choose from.
This board basis is popular with couples and small groups of people. Bed and Breakfast will allow you to go off throughout the day and explore the resort/local area, go out for evening meals as well as trying out all the local and traditional cafes for lunch.
Self Catering means that no meals will be included within the price of the holiday, but you will be provided with catering facilities including a fridge in your accommodation to cook meals. With self-catering holidays, you have the freedom to eat and drink wherever you like with the luxury of exploring the culture and nightlife of your destination to boot. If you are a couple, or in a group where everyone pays for themselves, self-catering can be a great option.
Room only specifically means that there are no meals included, you are just paying to stay in the room (note it is unlikely there will be cooking facilities in the room). So if you want breakfast or an evening meal you have to pay for these. All the other amenities of the hotel are there for your use as a guest.