PDF Forms are a special kind of PDF documents containing form fields. Some PDF tools (e.g. Adobe® Reader) support filling in these PDF forms on the screen.
Annotations created in PDF Annotator, which overlap with form fields of a fillable PDF form, would usually get covered by those form fields in other PDF applications. In the result, those annotations would only be partially visible, or not visible at all.
For that reason, when you open a PDF form, PDF Annotator offers these options in the The document contains form fields dialog:
When you choose Remove form fields, all form fields will be removed. Existing form entries will get converted to regular text in the PDF document.
Now, all PDF Annotator tools (like pen or marker) can be used, like on any PDF document. Annotations created in PDF Annotator will now (like you're used to) cover the original PDF content.
When you re-open the document in a PDF application supporting fillable PDF Forms (e.g. Adobe® Reader), there are no fillable form fields available any more. The document is not a fillable PDF Form any more.
In the picture: (1) The PDF Form in Adobe® Reader, (2) the PDF document opened in PDF Annotator using the Remove form fields option, (3) an annotation created in PDF Annotator, and (4) the PDF document saved by PDF Annotator and re-opened in Adobe® Reader. The annotation created in PDF Annotator covers the previous form fields. Form fields are not fillable any more.
When you choose Preserve form fields, the form will stay as is. It can still be filled in applications supporting this - even after adding annotations in PDF Annotator.
But, if annotations created in PDF Annotator overlap with form fields, those annotations will usually get covered by the form fields when viewed in other PDF applications (e.g. Adobe® Reader).
In the picture: (1) The PDF Form in Adobe® Reader, (2) the PDF document opened in PDF Annotator using the Preserve form fields option, (3) an annotation created in PDF Annotator, and (4) the PDF document saved by PDF Annotator and re-opened in Adobe® Reader. The annotation created in PDF Annotator is now covered by the form field. The form can still be filled out.