In Views, how can I show only the results for content that has been tagged with two taxonomy terms? I'm using Drupal 7:

I have a taxonomy term view that uses two contextual filters (i.e. taxonomy/term/%/%). Under 'Relationships' I have selected: 'Content: Taxonomy terms on node'. Under this relationship I have selected two vocabularies. Under 'Contextual Filters' I have selected: '(terms) Taxonomy term: Term ID'. Within the contextual filter I've selected 'Display contents of "No results found"' under 'WHEN THE FILTER VALUE IS NOT IN THE URL'.

The reason for two contextual filters is because the content is tagged with two term reference fields each of which correspond to a different taxonomy vocabulary.

The problem is that the results I get are not filtered by the second taxonomy term.

For example, if some content has been tagged with 'board of directors' (tid = 29) and 'people' (tid = 34) then everything that is tagged with 'board of directors' displays under taxonomy/term/29/34 even if they have not been tagged with 'people'. 

How can I configure my view so the results are filtered according to two taxonomy terms?
I'm not sure why are you using Relationships for this. Simply, from "Contextual Filters" section, create a "Content: Has taxonomy term ID". In that filter's settings -> "More" settings -> Check "Allow multiple values" which: 


  If selected, users can enter multiple values in the form of 1+2+3 (for OR) or 1,2,3 (for AND).


i.e. go to view_path/29,34 will filter results by both terms.

Hope this helps.