If you speak to anyone in an organisation, they will have differing views as to what it means to them - there are just too many elements in play (from Big Data, Cloud, Social Networks, AI etc) and at too many levels within the organisation.
I believe it needs to be aligned in some old-school business terms:
The market is now expecting an enhanced or new product. It may be richer, have more insight, integrate existing services, support collaboration with the client etc. But if you don't do it, your days as a business in this market are numbered; if you do it right, someone else takes the hit.
The delivery is usually any time, any place, any device, usually via cloud services in some fashion, with security and social elements adding interest. Often alongside existing channels, though you might be able to remove these.
The operations component being the back-office elements needed to deliver the above, preferably making use of some of the technologies used above. This is still the tough bit - business change, with new technologies/experimentation, new skills and capabilities needed, and the handling of client feedback - without upsetting the client, and without blowing the budget.
'Digital' scope will need to be prioritised with the Board so that the business can handle the change and the right parts are delivered first. And bear in mind the market will move on by next year so priorities will change...