A common way to define institutions is to treat them simply as organisations that tend to persist over time. A stricter definition, and closer to the one we use here, is to treat them as the noun form of the verb root: "to institute," i.e., to put into practice, to habituate. Thus, one meaning of institutions in the Oxford English Dictionary is "the giving of form or order to a thing; orderly arrangement; regulation." Related to this is "an established law, custom, usage, practice, organisation, or other element in the political or social life of a people; a regulative principle or convention subservient to the needs of an organised community or the general ends of civilization."
The following definition of institutions is taken from Douglass North's 1993 Nobel Prize Lecture:
"Institutions are the humanly devised constraints that structure human interaction. They are made up of formal constraints (rules, laws, constitutions), informal constraints (norms of behaviour, conventions, and self imposed codes of conduct), and their enforcement characteristics. Together they define the incentive structure of societies and specifically economies."
One needn't be wedded to New Institutional Economics to find this characterisation useful for understanding the circumstances under which corrupt practices can flourish. Rather, in the context of corruption, it more broadly expresses the milieu of both formal and informal--and economic and social--incentives and penalties in which individuals and social groups typically make decisions as to whether or not it is worth engaging in corrupt behaviour.