Generally, either the study of being, or a particular theory of what there is (as in 'Smith's ontology contains classes but not propositions', meaning that Smith believes there are such things as classes but not such things as propositions).
More specifically, part of the logical system underpinning the mereology of Polish logician Stanislaw Lesniewski (1886-1939). The system uses three types of names -proper names ('Socrates'), common names ('dog'), and fictitious names ('Apollo', 'centaur') - and elaborates the relations between a complex set of connectives that can be applied to them; for example, 'is a' ('Socrates is a man'), 'overlaps' ('Some cats are pets'), and so on.
The other part of Lesniewski's logical system is called protothetic, a sort of generalization of the standard logic of propositions.
C Lejewski, 'On Lesniewski's Ontology', Ratio (1958)