The Merriam-Webster's Learners' Dictionary defines 'participation' as follows:
to be involved with others in doing something; to take part in an activity or event with others
As such, the key feature of 'participation' is 'involvement', with the verb 'to involve' defined as
1a : to have or include (someone or something) as a part of something; b : to cause (someone) to be included in some activity, situation, etc. : to cause (someone) to take part in something; c : to cause (someone) to be associated with someone or something
2 : to require (something) as a necessary part
3 : to affect (something)
What participation means for institutions still widely regarded as sanctified repositories of knowledge entrusted with the maintenance of records and archives and the collection and stewardship of historical artefacts (yes, that's museums!) may mean was extensively explored in Nina Simon's The Participatory Museum (Santa Cruz: Museum 2.0, 2010). As she explains in her book's chapter 1: Principles of Participation
How can cultural institutions use participatory techniques not just to give visitors a voice, but to develop experiences that are more valuable and compelling for everyone? This is not a question of intention or desire; it’s a question of design. Whether the goal is to promote dialogue or creative expression, shared learning or co-creative work, the design process starts with a simple question: which tool or technique will produce the desired participatory experience?
Designers have answered versions of this question for many kinds of visitor experiences and goals in cultural institutions. Professionals know how to write labels for different audiences. They know what kinds of physical interactions promote competitive play and which promote contemplative exploration. And while they may not always get it right, they are guided by the expectation that design decisions can help them successfully achieve content and experience goals.
When it comes to developing participatory experiences in which visitors create, share, and connect with each other around content the same design thinking applies. The chief difference between traditional and participatory design techniques is the way that information flows between institutions and users. In traditional exhibits and programs, the institution provides content for visitors to consume. Designers focus on making the content consistent and high quality, so that every visitor, regardless of her background or interests, receives a reliably good experience. [...] In contrast, in participatory projects, the institution supports multi-directional content experiences. The institution serves as a “platform” that connects different users who act as content creators, distributors, consumers, critics, and collaborators. This means the institution cannot guarantee the consistency of visitor experiences. Instead, the institution provides opportunities for diverse visitor co-produced experiences.
while in chapter 5: Defining Participation at Your Institution, Nina Simon uses a series of categories defined as part of a research developed in the Public Participation in Scientific Research (PPSR) project at the Center for Advancement of Informal Science Education (CAISE) to further detail participation boundaries in an institutional context:
The PPSR report defined three broad categories of public participation in scientific research: contribution, collaboration, and co-creation. [...] Like science labs, cultural institutions produce public-facing content under the guidance of authoritative experts. Therefore the three PPSR models for public participation can be applied directly to cultural institutions, with some slight changes in language:
In contributory projects, visitors are solicited to provide limited and specified objects, actions, or ideas to an institutionally controlled process. Comment boards and story-sharing kiosks are both common platforms for contributory activities.
In collaborative projects, visitors are invited to serve as active partners in the creation of institutional projects that are originated and ultimately controlled by the institution. [...]
In co-creative projects, community members work together with institutional staff members from the beginning to define the project’s goals and to generate the program or exhibit based on community interests. [...]