Heterogeneous stream formats, related contexts, vocabularies and schema structures are key difficulties to facilitate sharing and extracting knowledge from stream databases. To resolve these heterogeneities, the key challenge is how to provide common semantic representation for context-dependent data stream formats along with streaming databases. To address such issues, this paper proposes an ontology driven formal semantics of context-dependent data streams together with a universal conceptualization of streaming databases. The novelty of this work is to handle heterogeneity, large volume and availability of streaming data, such as web content, commercial broadcasting data etc. It also facilitates to recognize evolving information from semantic representation of data streams at conceptual modelling level. Besides, the proposed conceptual model is flexible to represent finite partition of stream and thus help in data stream storing and further querying. The conceptualization is implemented using an ontology editorial tool Protégé for the initial validation of proposed set of formal semantics. Several crucial properties of the proposed conceptualization are specified in order to exhibit the benefits of the proposed work. The expressiveness of proposed model is illustrated using a suitable case study.