Clicking a taxonomy term in a Node leads to a URL like
taxonomy/term/7 with a list of nodes with that taxonomy term. However, my Drupal installation is only showing 3 nodes/page in that list. Is there a way to customize the number of results the default taxonomy term search shows?
The Views module has a default View for that page. If you enable it you can adjust it the way you want like you would normally do with Views.
Without Views: see comments.
The root cause of your problem is because of a setting found here: admin/config/system/site-information. This is the admin page for setting 'site' information, such as the site name, email address, etc.
One of these settings is called 'Number of posts on the front page'. Changing this value changes not just the front page but ALL taxonomy term display pages.
This is why you were only seeing 3 posts. Using the Views option to override the default Drupal taxonomy term pages is a good option, but it does have some side effects. For example, I'm not sure in D7, but in D6 I noticed that I lost the ability to filter terms on these pages when using the Views override. In D7, I lost the ability to display on the term page any fields including the term description associated with that taxonomy term.