Where exactly does the edit_{taxonomy} hook fire?

^{Please have a read on how to work with filters and actions (I’m not repeating it here).}

The filter in a theme or plugin

// inside /wp-includes/taxonomy.php on line 1586
$value = apply_filters("edit_{$taxonomy}_{$field}", $value, $term_id);

// inside some theme file that runs before - best on functions.php during your themes bootstrap:
function wpse40709_edit_tax_field( $value, $term_id )
{
    // Do modifications

    return $value;
}
// Should be hooked in bootstrap, so best would be 'after_setup_theme' until 'admin_init'
add_filter( 'edit_YOUR-TAXONOMY-NAME_YOUR-FIELD-NAME', 'wpse40709_edit_tax_field', 20, 2 );

The filter in core

The filter gets triggered, when

sanitize_term_field($field, $value, $term_id, $taxonomy, $context)

runs. So the $field is whatever name your field has.