Structuralism is the theoretical point of view (especially in humanities) which emphasises that the entities considered are parts of a system and that their very meaning and identity is defined according to its relation to the rest of the system. If one part of the system changes in time all other parts change as well. The system has features which are not just the added features of its constituents. The structuralism is devised as an influential direction in science in 20th century with Ferdinand de Saussure (and later Roman Jakobson) in linguistics, Claude Lévi-Strauss in anthropology and so on.
To some extent, the point of view of category theory is similar: one talks about properties invariant under isomorphisms; from the point of such an object is determined by the morphisms to or from other objects. Manin says that the category theory takes objects as part of a “society”.
To some extent Bourbaki’s emphasis on mathematics as the science of abstract structures has earlier also taken a similar point of view where structures are important only up to isomorphism and the emphasis is on relations (including) functions which are part of the “structure”.
Colin McLarty, 2004, ‘Exploring Categorical Structuralism’, Philosophia Mathematica, 12, 37–53.
Jean-Michel Kantor, Bourbaki’s Structures and Structuralism, The Mathematical Intelligencer 33:1 (2011), 1, doi