In order to “edit” a PDF file in Acrobat, you must install the fonts used in the document on the system doing the editing. For example, suppose you create an InDesign document using the font Glurbish Modern which you have installed on your system and you export that document as a PDF file.
If you provide that PDF file to someone else and they want to use Acrobat's Text Edit feature, they must install the Glurbish Modern font on their system in order to do edits of text formatted with that font! (Acrobat does not use any embedded fonts for this text edit function!) And no, you can't simply give those font files to the person doing the editing unless your font's EULA (End User License Agreement) allows for that!
As always, be aware that Acrobat's Text Edit functionality is really designed for text “touch-up” as opposed to providing anywhere near full text editing functionality such as you have in InDesign!
- Dov