"Fully furnished" means the apartment or house you are renting comes with all the built-in and loose furniture, white goods (refrigerator, washer and dryer) and all other essential electric appliances.  

"Partially furnished" apartments or house usually only comes with white goods, curtains, lightings, wardrobes and kitchen cabinet.

Although a house may be partially furnished at the time of viewing, you can always request the landlord to fully furnish it or request him to get specific household items you may require. All these are done during the negotiation period and will subsequently determine the final rental amount.