The DER file extension is primarily associated with a DER- (Distinguished Encoding Rules) encoded X509 digital certificate file.
A digital certificate is issued by a certification authority (CA) and contains a certificate holder's name, a serial number, expiration dates, a copy of their public key (used for encrypting messages and digital signatures), and the digital signature of the certificate-issuing authority to verify that the certificate is valid.
SearchSecurity.com explains the public key infrastructure (PKI) and digital certificates.
Randall Gamby discusses digital signatures and digital certificates.
Also from SearchSecurity.com, here's a collection of news and learning resources about digital certificates.