My father was a management consultant for many years. As I understand it, it's a lot like the work of efficiency expert Frank Gilbreth (the father in the original "Cheaper by the Dozen") as applied to management.
Many companies, as they grow, have legacy management behaviours that are inefficient, to put it mildly. A managerial consultant looks at these from the outside, points out what isn't working, and finds a better, more efficient (and often money-saving) way. They're often responsible for management restructurings at a company that results in a "leaner" team (i.e. cutting management jobs).
One of my favorite examples of my father's was the Mississippi barge company. They used a roster of where the tugs needed to be and when, but if anything was running late (and it usually was), tugs would sit idle for days at a time waiting for barges. My father rode with several of them, getting a feel for the process.
His solution? Call ahead. He had all the tugs fitted with special radiophones (this was the early 70's, new technology!) and a dispatch system so that if a set of barges was running behind, the waiting tug could be freed up to go back to port and take a different load, and a later tug could meet the late barges. Downtime was cut by huge amounts, and the amount shipped went way up. Efficiency!
He got the idea when he was jumping off a tug at a lock to call home one evening. It was a regular ritual, and he could only talk until the tug was getting ready to leave the lock so he could hop back on... "why the hell can't there be phones on the tugs?"
So sometimes it was actual process efficiency, but a lot of the time it was just streamlining the management process. Some companies liked what he did so much they hired him away from the consulting company - this happened three times, and each time he turned the company around to the point where they were bought out by a competitor... and he'd be out of a job in the reorganization, and go back to consulting.
So if you're a killer at analysing, and you like coming into a new environment and shaking things up to improve them, it can be an amazing job. Lots of travel, too. Dad always arranged to be home weekends, though. Many of the consultants didn't - just lived out of a company-provided hotel room for weeks at a time, until a job was done.
Anyway, hope that helps a little!
Edit: I see you've already decided... yeah, it's not the life for everyone.