I enter data in the fillable fields and save the document as a pdf file. I sent it to someone who opens it using an iPhone or iPad and the content of the fields is not visible.
Did you send your form as an email attachment?
It is highly likely that the email recipient opened your PDF form in Apple Mail on an iPhone or iPad.
Please note that Apple Mail's preview does not show filled form data or annotations (Sticky Notes, Highlight, Freehand drawing, etc.) in a PDF document. It's the known limitation in Apple Mail, iBooks, and Safari.
You can ask the email recipient to install Adobe Reader for iOS and use the "Open In" feature to open it in Adobe Reader.
Please take a look at the Mail section of the FAQ documents for the instructions on how to use "Open In".
Please let us know if you have additional questions.