According to Robert Merton manifest functions are those that are intended and recognized. These are functions which people assume and expect the institutions to fulfil. For example schools are expected to educate the children in the knowledge and skills that they need. The manifest functions are obvious, admitted and generally applauded. Latent functions are unrecognized and unintended functions. These are the unforeseen consequences of institutions.
For example schools not only educate young they also provide mass entertainment. Latent functions of an institution or partial structure may support the manifest functions for example the latent functions of religious institutions in the modern society include offering recreational activities and courtship opportunities to young people. Latent functions may be irrelevant to manifest functions for example the big functions organized by schools may not impact the purpose of the education.
Latent functions may even undermine manifest functions. For example the manifest function of civil service regulations is to secure a competent dedicated staff of civil servants to make government more efficient. But the civil service system may have the latent function of establishing more rigid bureaucracy. The distinction between manifest and latent functions is essentially relative and not absolute. A function may appear to be manifest for some in the social system and latent for others.