Context-aware application plays an important role in the ubiquitous computing (ubiComp) environment by providing the user with comprehensive services even without any explicitly triggered command. In this paper, we propose a unified context-aware application model which is an essential part to develop various applications in the ubiquitous computing environment. The proposed model affirms the independence between sensor and application by using a unified context in the form of Who (user identity), What (object identity), Where (location), When (time), Why (user intention/emotion) and How (user gesture), called 5W1H. It also ensures that the application exploits a relatively accurate context to trigger personalized services. To show usefulness of the proposed model, we apply it to the sensors and applications in the ubiHome, a test bed for ubiComp-enabled home applications. According to the experimental results, without loss of generality, we believe it can be extended to various context-aware applications in daily life.