With Mandrill you can create highly customized messages to send to recipients based on a specific action you're tracking in your app (registration date, purchase date, or product purchased). This is very similar to Mailchimp's Automation feature, but with Mandrill all of the logic about who should get an email, when they should get it, and what it should contain would be handled in your own system and passed to Mandrill at the time of send in your API request or SMTP message.
For example, if someone registers on your website and you want to send them an email immediately, you'd need to program your system to send that information to Mandrill as it happens. If the recipient should get another email one month later, your system would store that information and when it's actually time to send the second email, it would be passed over to Mandrill at that time.
You can also schedule emails to send at a later date and time, and Mandrill will store those emails for you.