What is DKIM?
DKIM stands for DomainKeys Identified Mail. It's an email authentication protocol, using digital signature attached to the header of email. In a nutshell, when DKIM is published in the DNS records of a domain, it will display a public key that the recipient email servers can match with the encrypted key in the signature.
The receiver to check if an incoming email is authentic (i.e. hasn't been modified by any third party since being sent).
The receiver to verify that the email has been sent from an address associated with the right sending domain.
The sender to prevent "domain spoofing".
Why is it important?
As for any email authentication protocols, having DKIM properly set improves the deliverability of emails sent from this domain. Indeed, some email servers can block the access to email with no DKIM record published.
In the same way, your domain has less chances to be blacklisted or have a bad SpamAssassin grade if it has a DKIM record published.
In a nutshell, having DKIM properly setup will make your emails more secure while increasing your deliverability.