Transactional emails can be used in a number of ways as they are basically emails that are triggered by an action or inaction.
Essentially, you can use transactional emails whenever you have a situation where a client could possibly trigger a response from you or your company.
For example, when a customer signs up to receive regular email updates from your company, that signup action can trigger a transactional email to be sent, thanking the customer for signing up and asking them to provide further confirmation.
Another easy way to use transactional emails is whenever a client purchases a product off of your website, that could trigger a transactional email with the client's purchase receipt as well as any shipping information that is available. You could also use these emails to suggest other products that the customer may like, based on what they have just purchased.
On the other hand, you could use a client's inaction to trigger a transactional email. For example, if you have sent a client an email with important information in it that is time sensitive, you could set your campaign to send a second transactional email to the client, triggered only if they have not opened the email after a certain length of time.