What are Text Filters and Input Formats? In views, when I add a field of type body, there are some options given: text_default, text_plain, text_trimmed.

How do these options filter the contents of the field and where can they be found in the code??
These are called 'text filters', and a text filter is made up of 'input formats'. Input formats are defined in hook_filter_info().

You can read more about text filters here: https://www.drupal.org/node/213156