A hackathon is a creative process where programmers try to create a solution based on a challenge put to them in a certain amount of time, usually 24 - 48 hours. The concept is not unique to the open data, having come from computer programming community around 20 years ago.
A hackathon is a design sprint in which computer programmers, often joined by designers, analysts, researchers (and other subject matter experts and people from other disciplines based on the theme and context) collaborate to build a software and/or hardware solution, usually based around a set focus, industry, technology or technique.
Within open data initiatives, hackathons are particularly useful as explorations into what end-user tools can house a dataset or a group of related datasets. For example, to follow through the other forms of engagement, if a unconference focussed on mobility revealed the need for real time public transport information, and a dataquest around public transport data from a city revealed that bus transport data and buses as a mode of transport are of particular interest to citizens, a hackathon may see a team of transport experts, programmers and designers building a "where is my bus" app which citizens can download on their mobile phones, and which serves them real-time bud route, timing and location information.
The video below is of a hackathon held for the Open Government National Open Data Portal with the Department of Public Service and Administration in 2015.
Hackathons should be fun, high energy events that drive public engagement with civic data and information, and get attendees to put themselves in the shoes of a resident of the city and try to identify with, and solve for, their problems. Every now and then a useful solution will come out of a hackathon, but this will usually then require a lot of support and resources post the hackathon if it is to reach fruition. As in the case of a dataquest, understanding and insight into potential use cases for public information and data, and the civic interaction and engagement at an open data hackathon are likely to have more impact that the actual solutions created.