The corresponding member is one of the possible membership types in some organizations, especially in the learned societies and scientific academies.
Because such people were unable to attend meetings, for organizational reasons they had to communicate their scientific contributions by "correspondence".
So, for example, the Australian Academy of Science entitles the prominent foreign researchers only to corresponding membership; among the people with this status are David Attenborough (United Kingdom), Rolf M. Zinkernagel (Switzerland), Elizabeth Blackburn (USA) and Gunnar Öquist (Sweden).
For example, in the Academies of Science in some post-Soviet states (e.g., Russia, Belarus, Ukraine), following the custom of the Academy of Sciences of the USSR, a scientist is usually first elected to the corresponding membership and several years later, if he (she) demonstrates new outstanding achievements, to the full membership.
In some organizations, “corresponding” membership may be preferred by an applicant (which can be an individual or a legal entity) itself.