Part of this is triggers, which seems to be the focus of a lot of the discussion here, but an even bigger piece is personalization. The idea with personalization is to show the user content that is relevant to them. That involves a big analytics and prediction component in terms of figuring out their context, and their interests. We've seen some pretty crazy results in terms of jumps in engagement that emerge from personalizing emails to users, and also engaging users at the right points in time, in the right ways. This is relevant to the triggers conversation as well, in terms of being able to identify and personalize the triggers for each user. We haven't run explicit experiments on that aspect in terms of magnitude, but a trigger system in a vacuum won't give you the same type of power as a personalized/automated one.
Even things like personalizing WHEN you send an email to a user have a dramatic effect on open/click rates. One of our clients experienced a 10% increase in revenue (they were already making substantial revenue) by leveraging Horizon Send Time (Our product that sends an email to a user when they are most likely to open based on that users previous open habits).
The right combination of personalization to users, and appropriate event-based triggers, can really improve the perception of users (oh wow the content being sent to me is actually valuable!), and increase their happiness, and subsequently their life-time value.