Benjamin was very interested in culture and what it could tell us. Culture here does not mean 'high culture' (art, literature, opera, etc) but the more mundane artefacts of the quotidian; posters, prints and printing, cinema, TV, and everything that one encounters in daily life. Indeed all of the ephemeral and evanescent stuff that we could absent-mindedly throw away or forget about whether it be material or conceptual (i.e. small-talk or other conversation). Indeed Benjamin's most important work - The Arcades Project - is specifically concerned with what all of this seemingly throw away stuff could tell us about the history of Paris in the 19th century and thus about the history of the 19th century more generally.
For our purposes - the study of the media and of society more generally - this concern with culture is very useful (Benjamin's concern with culture prefigures Stuart Hall and the CCCS and is therefore an essential point of contact). Benjamin was a member of the Frankfurt School and so was also concerned with the role and function of power and domination in society. This can be most clearly seen in his critical analysis of the Haussmannization of Paris in his Paris; Capital of the Nineteenth Century. This 'renovation' (we would call it 'urban regeneration' today) of Paris in the period of the Second Empire was seen by Benjamin to be a means of controlling the urban space (the great wide boulevards that Haussman's project introduced were far harder to barricade) and of policing its people by forcing the poor from the centre into the periphery.
Benjamin's most famous essay - on The Work of Art in the Age of Mechanical Reproduction - helps us to think about and understand a lot of the issues involved in the current media landscape. Benjamin's argument in this essay is simple; the ease with which 'art' can be reproduced and disseminated is democratic.
This needs some expansion;
The ease with which 'art' (which we can take to mean cultural artefacts of any kind)
can be reproduced, either mechanically (printing, photography, photocopier, cd/dvd burner) or digitally (computer, digital photography, scanner, etc),
and disseminated, again either mechanically (post, courier, etc), institutionally (library, etc) or digitally (TV, Internet, BitTorrent, etc),
is democratic (benefits the people and breaks down the structures of domination in society).
Benjamin welcomed the very problem faced by contemporary media corporations whereby they spend a great deal of money creating a media artefact that then costs nothing to digitally reproduced & disseminate (given the existence of, and access to by the participants, the astonishing communications infrastructure we call the internet).
The current political problems around the Digital Economy Bill [here, here & here] are exactly concerned with the problems that Benjamin identified. The efforts of the Big-IP combines (the big four, the big six, the other big six, etc) to turn state power to the effort to control their property and thus defend their profits against the democratizing effect of the reproducibility of culture.