You will receive push notifications in the following scenarios:
Someone likes your transaction that was posted in the Social feed.
Someone comments on your transaction that was posted in the Social feed.
A message is sent to you by one of the users who follow you and you follow them back.
You have received a follow request from a Shares user.
In each of the cases mentioned above, you can simply tap on the push notification, and the app will open the appropriate screen for you to review these actions.