Element API using the entries field to display related content from a separate section
If relatedJobDescription is an Entries field, accessing the field from your jobs entry will not return the selected jobDescriptions entry directly. Instead, you will get an EntryQuery which you can use to get the selected jobDescriptions from the database. See Working with Entries Field Data and Querying Entries.
To get the jobDescriptions entry, you can use ElementQuery::one() (if your field allowed for multiple related jobDescriptions entries, you could use ElementQuery::all() instead).
Regarding the descriptionOverride, that's just a matter of checking if the override field contains some text and if it does, return it instead of the related job description.
Something like this should work:
// get the entry holding the related job description
$relatedJobDescriptionEntry = $entry-&gt;relatedJobDescription-&gt;one();
// handle an empty relatedJobDescriptions field gracefully
$relatedJobDescription = $relatedJobDescriptionEntry ? $relatedJobDescriptionEntry-&gt;description : '';
// get the description override from the current entry
$descriptionOverride = $entry-&gt;descriptionOverride;
return array(
    'title' =&gt; $entry-&gt;title,
    // return either the overridden description or the related job description
    'description' =&gt; ((string) $descriptionOverride) ?: $relatedJobDescription,
);

You can optimize this further to only retrieve the related job description if the override is not set.