Selecting “Export households” in the Details tab of a Transaction, Interaction, Note, or Task report means that if any individual meets your filter criteria that is linked in a household, the name and profile info will display from the household record and not the individual. Also, if more than one individual in the same household meets your filter criteria, only the household record will display, not each individual.
It may be helpful to think of it like this: if John and Jane are in a household together, and you run a report that includes filtering that includes Jane but excludes John (or includes both), exporting to household will cause John and Jane’s household to appear on the report (since Jane meets the filter criteria or both). This behavior is the same for letters as well when using the One Letter Per Household option.
Changing the filters in a Constituent report from Constituent to Household means that the filters will look at the combined household to determine includes/excludes, and will display the household record if it meets your filters, not each individual record.