In genealogical research, what is the difference between primary information and secondary information. Why do genealogists bother with making such distinctions?
Primary information is information provided by a reliable participant in, or eyewitness to, an event, or by an official whose duty was to record the event details accurately and in a timely manner.
There's an excellent description of the concepts of primary and secondary information, original and derivative sources, and direct and indirect evidence at the Board for Certification of Genealogists site; see http://www.bcgcertification.org/skillbuilders/skbld085.html
Primary information is information about an event (e.g., a birth) that was obtained at the time of the event, and therefore is considered a much more reliable record of the event. Information about the same event that is recorded at a different time (e.g., a date of birth on a death certificate or on a tombstone) is less reliable because the person providing that information may have had incorrect information for any number of reasons.
Thus primary information is more reliable than secondary for establishing facts about the people you are researching.
I am not sure that there is a useful distinction between primary and secondary information. Historians refer to primary and secondary sources with the definitions that have been used in the other answers.
See this document from Princeton University
All information is information but the weight that we give it may vary with the quality of the source that contains it. A birth registration is a primary source when the details are provided by a witness to the event (such as the midwife). Exactly the same information about date and name may be found in the local newspaper but that secondary source is (potentially) less reliable because the journalist was not there.