Of all the skills a consultant brings to the table, sometimes the actual discipline for which you've been hired is the least important.
I have been a consultant, first in an agency, then on my own, for five years. In that time, I've worked in a number of companies, from non-profits to Fortune 100s. When a company brings in an agency or consultant, it's usually because they don't have the available resources or the skills in-house. What may surprise though, is how often that skill gap is not in technical skills or design skills or project management and delivery—or is not only in those, anyway—but in communication. Often I have been in the position of introducing one member of a company to another member of a company—literally being the liaison who makes the connections between organizationally separated (and sometimes even geographically separated) teams with common interests and need for shared outcomes but no organizational structure or incentives for collaboration.
Sometimes those distances are enforced by the virtual walls that silo different areas of an organization—IT from marketing is a typical example. Take a legacy of non-communication, add a failed project or two (refer back to that non-communication), and an ever-widening gap of mistrust opens up within the organization and the consultant ends up being the diplomat who helps the factions reach a successful resolution.
When one area of an organization feels under-represented at the table and is stuck working with outdated tools and processes, another important role a consultant can play is to simply listen. I have spent many hours with employees who are just grateful to have someone to describe their situation to and finally feel as though they've found a sympathetic ear. My job, of course, is not just to listen, but to document and plan and work with the other side as well as my consulting colleagues to create solutions that address not just the technical or procedural issues but the communication issues within their companies. When a client cries to see you leave at the end of a project, you know that consulting is as much about organizational psychology as it is about implementing new features, tools, or websites.