If enabled, digests will indicate if it sent the digest in the admin log. If it says it sent it but they did not arrive, the problem lies elsewhere. They may end up in a spam folder, for example, or your web host may be blocking them from going out because they think it might be spam.
Digests use phpBB's mailer, which uses PHP mail or SMTP if your forum is configured that way. If an email package size is set, they may be in a queue to go out.
The first post talks about depending on board traffic vs. a system cron. If there is no board traffic, they won't go out until there is board traffic.
If it says nothing was sent because filters meant there was nothing to send then the issue is a filter. Most typically it is because there are new posts in the forums requested. The list of possibilities is in the earlier link.