A biobank is a physical place which stores biological specimens.
Access policies details may vary across biobanks but generally involve obtaining ethics approval from institutional review boards (IRB) and scientific review or peer review approval from the institutions under which the biobanks operate as well as Ethics approval from the institutions where the research projects will be undertaken.
The samples and data are safeguarded so that researchers can use them in experiments deemed adequate.
Some examples of how they can be classified is by their controlling entity (government, commercial enterprise, or private research institution), by their geographical location, or by what sorts of samples they collect.
[1] Population-based biobanks need no particular hospital affiliation because they sample from large numbers of all kinds of people, perhaps to look for biomarkers for disease susceptibility in a general population.