The connectivity model is highly generalized, abstract model that allows communication with variuos data sources, without having to know upfront about their implementation details.
If you know ODBC, OLE DB or such technologies for database access, then you can think of Connectivity Model as a similar technology, but for live data, such as in industrial automation or related sectors.
QuickOPC currently does not make the programmatic access (API) to the Connectivity Model public. The Connectivity Model is, however, on the basis of Live Binding Model, Connectivity Explorer tool, and Excel Option (RTD Server). All these QuickOPC parts share the features provided by the Connectivity Model, and take advantage from the fact that the model hides the differences between the supported connectivities, such as OPC Classic or OPC Unified Architecture.