DER is a binary format for data structures described by ASN.1.
by example x509 is described in ASN1 and encoded in DER. It exists other encoding formats for ASN.1 but DER is the one choose for security since ther is only one possible encoding given a ASN.1. encoding ( what is not the case for BER used in ldap by example ).
openssl *asn1parse* is the command to display internal structure of a DER document.