It is quite exciting to be based for a couple of months in India or Japan, manage a multi-cultural team, and advise the CEO of one of the top companies in the country!
The team problem-solving is some of the most fun, interesting business work out there. Getting a bunch of smart people around a white board to brainstorm solutions and work through complicated issues together is very compelling.
Also, at a younger professional age, you often work with very senior-level clients on very high-level projects. Otherwise would be difficult to access this type of project until much later in a career.
Leading a team and witnessing each person's development. Ability to have major impact at a client's strategic priorities. Exposure to senior management at Fortune 500 companies. Develop a broad skill set that is applicable to any industry/business.
More than your resume, hiring managers want to see the thinking you'll contribute day one.
Learning about the types of jobs that exist shouldn't depend on who you know. You can change that.