I always ask this question at the beginning of a client engagement or workshop and it's amazing the range of responses you get back. People often talk about content, video, mobile, interaction, scale, ubiquity - frequently focusing on what digital does rather than what digital is. So one of my favourite definitions is to take the simplest possible definition and think about digital in terms of binary code - ones and zeros. A method of getting information from one place to another place that is not analogue.
The reason I use this is because it helps get past the idea that digital is a mysterious, amorphous, ever-changing thing that is impossible to grasp, and instead frames it in the context of taking common needs, wants, actions and delivering to them or applying them in a new way. Yes, digital technologies are radically shifting behaviours and reinventing entire markets, but that doesn't mean that we should forget everything we know about great products, great brands, great marketing, great content, great advertising.
It's often the case within organisations that there is a disproportionate focus on the technology itself (new technology for the sake of new technology), over all the stuff that surrounds the technology, really brings it to life, and fully realises it's capability (people, behaviours, processes, skills, culture). So I also rather like this definition from the team at Co-Op, which recognises that when done well, digital means more than fundamentally redesigning services, it also means changing the way in which we work: