There are broadly two reasons that the emails from the campaign you may have set up are not going through:
If there is an email limit set (i.e. number of emails that can go from your email ID in one day - best practice to avoid being flagged as spam) the campaign will stop for the day and send out the pending emails on the following day.
You may check the limit in 'settings', under 'general settings :
This basically entails any edits (such as adding a touchpoint) to a campaign after all the touchpoints have already been sent out to the candidate/contact - i.e. the campaign status is Finished on the candidate/contact.
Auto-delay between emails
Usually, there's a delay of 60-90 seconds between two emails going from the same campaign. However, if there are multiple campaigns running, the system will automatically send emails from each of the live campaigns once, before going back to the same campaign. Hence, in cases like this, there might be a delay of 5-10 mins between two emails going from the same campaign, depending on the number of live campaigns.
This is to ensure maximum open rates and delivery.