Expectation of privacy is a term which refers to an individual's right to be protected by the Fourth Amendment (protection from illegal searches and seizures) as long as they are in a situation where there is an expectation for them to have privacy. For example, an individual would have expectation of privacy for conversations they have or documents they possess within their home.
Basically, expectation of privacy means that law enforcement cannot search or seize anything without a warrant if the person is in a situation where privacy is expected. Expectation of privacy does not only refer to privacy within the home, but also in other situations where privacy is expected. For example, a conversation in a phone booth would give the expectation of privacy. Expectation of privacy does not apply to situations where information or evidence is being openly displayed to the public.