To do something secretly, privately to avoid controversy, disputation, or attention of a certain person, group, organization, company, etc...
1. "We need to secretly do this as carefully as possible, to be out off the eyes and ears of the people!"
^"People" in here could be the public or something like that and "we" here could be celebrities or any officials or thieves smt like that.
2."I got caught by my parents while buying CD games! Now I can't get/be out off my parents' eyes and ears!"
^In here "I" is the one who's talking, and the parent is the talker's dad and mom. In this situation, the talker is implying that his parent is now paying attention to him more so he doesn't do something that they don't want to, and their eyes and ears will always be there for him.
to be out off sb eyes and ears !