Take it from someone who used to be a fellow at Harvard at a couple of different institutes: they have their logic in handing out the title.  The Institute of Politics at the Harvard Kennedy School of Government lays out quite clearly what it expects its fellows, including the newly announced Chelsea Manning, to do.  Fellows are expected to hang out with students, faculty, and each other.

Fellows agree to be in residence for the duration of their fellowship, committing to be on campus Monday-Thursday each week throughout the semester. While at the Institute of Politics, Fellows are provided a fully furnished apartment on campus. Each Fellow works out of his or her private office at the Institute, complete with a computer and private phone.

The Institute of Politics offers a variety of public and private events that Fellows may enjoy. Fellows are expected to lead eight study groups and attend other Institute activities such as IOP Director's Dinners and weekly Fellows lunches. IOP Fellows act as mentors to students; therefore, each Fellow makes them self available for at least four hours of office time each week and often meet with students at other times that are mutually convenient. Fellows are invited and encouraged to attend as many other IOP events as possible.

The Institute of Politics provides spacious housing for Resident Fellows. A Fellow may bring his or her family to live in residence for the semester. The Fellows' apartments are conveniently located a short distance from the IOP (a ten minute walk). Additionally, spouses, partners, visitors and study group guests are invited to participate with the Fellows in IOP activities.

Fellows at the Institute of Politics are able to use all of the facilities of Harvard University: athletic facilities, libraries, museums, and other resources. Fellows are eligible to receive membership in the Faculty Club and may audit courses at Harvard College and other schools at the University. The Institute arranges for Fellows to meet the scholars, practitioners and participants of other centers at the University.

2016 Fellows (Photo via Harvard University).

Over time, as they meet people and encounter the resources the university has, some of them catch fire and form deeper and lasting ties with various members of the community.  Some of them are duds and don't come back.  But at a minimum, one year's worth of master's degree candidates in public administration are getting the opportunity to learn the thinking of the people they bring in.

This is the way Harvard works.  There are many, many different institutes salted throughout Harvard, with their own funding, that are able to bring in prominent outsiders from all over the world.  They can come as briefly as a talk, or they can stay for longer terms, using various titles that come with various responsibilities.

The Harvard brand name is so strong that lots of people of accomplishment or great promise can get drawn into the circle.

The Institute of Politics has so far announced three tranches of fellows.

May 31, 2017:

Harvard Kennedy School's Institute of Politics (IOP) announced today that Joe Scarborough and Mika Brzezinski, co-hosts of MSNBC's "Morning Joe," will serve as Visiting Fellows this summer and fall.

September 5, 2017: six more, including Mary Katharine Ham and Guy Benson and Corey Lewandowski, as well as former Kentucky governor Steve Beshear, whose bio on the announcement omits his party affiliation as a Democrat; Cornell William Brooks, "Visiting Fellow and Director of Campaigns and Advocacy Program"; and Joe Slade White, "an expert in creative television strategy and messaging, and has served as former Vice President Joe Biden's media consultant."

The latest:

Mayor Sylvester "Sly" James, Jr. is serving his second term as Mayor of Kansas City, Missouri after entering the office in 2011. ...

Chelsea E. Manning is a Washington D.C. based network security expert and former U.S. Army intelligence analyst. She [sic] speaks on the social, technological and economic ramifications of Artificial Intelligence through her [sic] op-ed columns for The Guardian and The New York Times. As a trans woman [sic], she [sic] advocates for queer and transgender rights as @xychelsea on Twitter. Following her [sic] court martial conviction in 2013 for releasing confidential military and State Department documents, President Obama commuted her [sic] 35-year sentence, citing it as "disproportionate" to the penalties faced by other whistleblowers. She [sic] served seven years in prison.

Robby Mook joins the IOP and Harvard community as a Visiting Fellow and Resident Scholar at Kirkland House for the 2017-18 academic year. Mook, a CNN political commentator, is a nationally recognized campaign manager and strategist who ran the 2016 presidential campaign for Hillary Clinton. He is currently a Senior Fellow with the new bipartisan Defending Digital Democracy project at the Belfer Center for Science and International Affairs. The project, also co-sponsored by the IOP and the Shorenstein Center on Media, Politics and Public Policy, will identify and recommend strategies, tools and technology to protect the democratic process from cyber and information attacks. (snip)

Sean Spicer served as Press Secretary and Acting Communications Director for President Donald J. Trump during the first half of 2017. Before he joined the White House senior staff, he was communications director of the Republican National Committee from 2011 to 2017, and its chief strategist from 2015 to 2017.