As mentioned, $_POST is not going to contain values you've fetched from the database, but rather, the data that's been POSTed to the script (from your form).
I assume that
<?php echo $bsiCore->getApmtTypeCombobox();?> is going to generate a number of
<option value="ID">Appartment Type 1</option>s.
<select> input, like you've got, will POST the
value attribute of the selected
<option> - in my example, the ID.
Normally, you'd store the id, and dereference it again later, to get the display value for that appartment_type, and so what you're seeing would be preferable. If you were building a multi-language site, you may need to join to a different table to get the display value, based on the language in question, so storing the string value wouldn't make sense.
If however, you do in fact want to get the string value of the appartment_type to be POSTed to your form handling code, then you'll need to adjust the output of
<?php echo $bsiCore->getApmtTypeCombobox();?> to use the value you want POSTed in the value attributes of the options (like
<option value="Appartment Type 1">Appartment Type 1</option>)
PS: There's only one "p" in apartment :)