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We often need to access and reorganize information available in multiple tables in diverse Web pages. To understand tables, we rely on acquired expertise, background information, and practice. Current computerized tools seldom consider the structure and content in the context of other tables with related information. This paper addresses the table processing issue by developing a new framework to table understanding that applies an ontology-based conceptual modeling extraction approach to: (i) understand a table's structure and conceptual content to the extent possible; (ii) discover the constraints that hold between concepts extracted from the table; (iii) match the recognized concepts with ones from a more general specification of related concepts; and (iv) merge the resulting structure with other similar knowledge representations for use in future situations. The result is a formalized method of processing the format and content of tables while incrementally building a relevant reusable conceptual ontology.