Turning 'potato' into 'puhtaytuh' is an example of what they're talking about. Saying 'puhtaytuh' involves less mouth movement than saying 'potato'.
Try using 'hot potato' in a sentence and you'll probably notice that the glottal stop at the end of 'hot' gets toned down or dropped. The 't' sound will still be there, but your tounge wont move as much as if you say 'hot' on it's own.