DLNA is an industry-wide standard for sharing data over a home network. Depending on the DLNA-compatible devices you own, you might be able to stream films from your laptop to your TV, play an MP3 stored on your phone over your hi-fi system, or print a photo from your tablet on your home printer.
DLNA stands for 'Digital Living Network Alliance'. It's a group of organisations, including many consumer electronics manufacturers, that has created a standard enabling all DLNA devices to share media over a home network.