Whether or not a Blu-ray player can access a home networked media server should be mentioned in its user manual.
AVR = Audio Video Receiver. It's a device which can take audio and video signals from many different kinds of players (Blu-ray players, CD players, Cable boxes, over-the-air and satellite radio, etc) to drive display devices (TV, projector, etc) and a surround-sound speaker system.
Many (but not all) modern AVRs include USB and network connections and can access a home networked media server as well as Internet entertainment services, as do many Blu-ray players.
BD = Blu-ray Disc
DLNA = Digital Living Network Alliance. They're an organization which has defined a standard for transmitting audio, video and pictures from media servers (including smartphones) to DLNA-certified output devices. DLNA media server software packages are available for computers. Some are free and some are commercial.