This question seems to bubble up everywhere. So here’s a quick primer.
If you DON’T work in education, a harbormaster is an official responsible for enforcing the regulations of a particular harbor or port, in order to ensure the safety of navigation, the security of the harbor and the correct operation of the port facilities. It’s the nautical version of an air traffic controller. I assume they look like this:

If you DO work in education, the term is a metaphor for a city-based nonprofit that plays a central role in funding and coordinating high-impact education initiatives.
The term was popularized by Ethan Gray, a Mind Trust team member who incubated and then launched Education Cities (formerly CEE-Trust — pronounced SEA-Trust), a member organization that convenes and supports harbormasters across the country. Education Cities is a current partner and former client.
Here’s how they describe the term:

The increasing number of harbormaster organizations in US cities indicates a growing interest in locally led improvement efforts. In an era defined by the perception of state and federal overreach, these organizations embody the notion that change should be driven locally. Harbormasters are staffed by local leaders with deep ties to their city who work in service of local students and educators. By aligning vision, resources, talent and political will, these organizations become the strategic leaders of their community’s efforts to create more great schools. They can also be the recipients of heated opposition from those who seek to preserve the status quo. Both are valuable roles.

We believe that there are four main elements to the harbormaster strategy: supporting quality schools, strengthening effective educator pipelines, advocating for pro-student pro-teacher policy changes, and ensuring authentic community engagement.

In concert, these four strategies create the conditions for high-quality public schools to launch, grow and persist. Harbormasters often lead in one or more of those areas and work in close collaboration with other local stakeholders on the other efforts to accelerate the pace and sustainability of school improvement. (Source)

Here’s a list of the Education Cities member organizations. Bellwether has extensive experience working with harbormasters including New Schools for New Orleans, The Mind Trust in Indianapolis, Choose to Succeed in San Antonio, Accelerate Great Schools in Cincinnati, and The Boston Schools Fund. (You can see our full client list here.)
We’ve learned a lot during these engagements. Most notably, the strategies they employ are highly dependent on the local education context. Some run a broad range of programs and carry a big staff to execute them while others are lean grantmaking organizations. Some primarily support charter schools while others employ a three-sector approach working with the local district, charters, and private schools. Some distribute their energy equally between all four areas described above while others focus narrowly on one or two. In most cases, however, harbormasters have a mission to buoy the number of high-quality seats in their cities.
For some education leaders, the term has run aground. They’re uncomfortable with idea of one organization “controlling” the education priorities in a city the way a nautical harbormaster decides which vessels dock where and when. Communities, they argue, should be the ones to have their hands on the rudder. The reality is that coordinating, funding, and influencing education initiatives and true community involvement aren’t mutually exclusive. The best harbormasters work tirelessly to understand the desires of parents and students and then use the best thinking from around the country to propel them forward.
So the term isn’t a perfect metaphor, but ideas floated during many ad hoc brainstorming sessions with colleagues close have come up dry. To their credit, Education Cities has expressed an openness to using a different term should one surface. If you have an idea for an alternative name, put them in the comments or tweet it to me.