What you are looking for are called "Remote Event Receivers" and they are only available in Provider Hosted Add-Ins (https://msdn.microsoft.com/en-us/library/office/jj220043.aspx.)
What you could do is implement a custom form within your add-in that is able to update the appropriate list items in your host web, as well as perform whatever logic is needed while updating those items.
If you want a page or app-part in your add-in to respond to a change in the host web while the page or app part is open in a browser, you could do something like poll the hostweb every few seconds, checking for the change. You may be able to use
GetListItemChangesSinceToken https://msdn.microsoft.com/en-us/library/office/dn292554.aspx, or just a simple query to the list. Be careful of querying too often for performance reasons, especially if the target list in the host web is large (>5000 items.)