Weird that I would get asked this, since it is on the sign above our building, and in the name of the degree for the program I direct, but I do. And, perhaps, with good reason.
First of all, if we are being pedantic, we could suggest that the proper question should be "what ARE digital media," since media is plural. But let's pretend that I am NOT a professor and prone to such nit picking. Ahem.
So, back to the question. What are digital media?
Media are tools we use to communicate.
I think everyone has a pretty good idea what media are. Humans use tools, and the tools we use to communicate across distances, across time and to more people at once than we could with our own voice and body are "media." Although the definition could include interpersonal and non-mass media, like the telephone, in common usage we typically have a sense that "media" are for communicating with more than just one person. Traditional examples include books, magazines, newspapers, film, radio, and television.
Digital relates to the use of computers.
Digital is even easier, in a sense, since it is almost entirely a technical definition and relates to the use of computers – with their "binary" language of on/off, 1/zero, bits and bytes. This is the digital world and includes computers, the software to run them, and the movement and storage of digital information via networks and storage (hard drives and cloud services).
So then is digital media just media with digital tools?
In a sense, yes, but in another sense, no. (See, academics are not just picky and pedantic, they equivocate).
If you put the radio on the internet, you certainly have digital media. And if you put a newspaper in a tablet, then you have digital media, as well. The problem with sticking with that definition is that it misses two important elements that have been made possible by the combination of computers, software, and networks: interactivity and group forming.
Interactivity is made possible because most computer networks are bi-directional and addressable. In other words, you can specify where your message is to go, and get a return message right away. This is a feature that is built into the telephone, but most mass media are one-way, or broadcast, media. They are engineered to deliver the same message to many people at once, but they don’t provide for any return messages. Digital media networks are different – you can still send the same message to many people (e.g., Netflix, or streaming radio, or just a simple web page), but you can also have interaction ranging from minor elements (choosing shows and rating them on Netflix) to major components (posting pictures and comments on other peoples’ photos on Flickr). For more on the value of interactivity in telecommunications networks, see the wikipedia entry on Metcalfe's Law.
The second unique feature of networked digital media is that – because it is based on software – the people participating in the network can organize themselves into ad-hoc and arbitrary groups. This is most obviously seen in Facebook, where you can instantly and easily create a new group around any sort of topic. These "group forming" networks have enormous value since they help us coordinate, communicate, and collaborate on projects large and small – from parties to promotion of brands.
When you look at it in this way, the most important parts of digital media are not simply the conversion of regular media to digital formats. That is the easy part. The hard part – and the part that unleashes tremendous value for society – is taking advantage of these new capabilities relating to interactivity and group forming.