Just a bunch of people
An Open Source project is people cooperatively improving a product. People from somewhere you never met or spoken to before, who want to help improve or change the project.
Contributors show up and they might have a different idea of what the project should do and will most likely have another driving force behind their commitment than you do. Because why would it be the same?
Most Open Source projects are formed around a name somewhere. Perhaps on a hosting platform that holds source code and offers project admin services. The name is not always unique, it is not always good and it is not always describing what the project actually does.
The project is rarely a formal or legal entity anywhere, at least as a start. Many projects that succeed, later grow up and turn into more formal organizations, or join other umbrella organizations to become part of them – and some are even run and owned by companies in the first place that then own the name and maybe even associated resources. But some projects remain collected solely under that name.
In most projects there is nothing formal to "join" when you want to start contributing. You usually just show up, ask questions, answer questions, submit bug reports or send in your proposed changes and improvements. When nobody has seen your name or contributions done by you before, you might meet a level of healthy skepticism and questions, but if you are well-meaning and do good, you will find friends and get accepted quickly in most communities. There is virtually no existing Open Source project that will not welcome and celebrate new and fresh blood contributing to the project.
Usually you get roles and responsibility over time by showing will and skill. Once you have proven yourself and the fact that you will stick around, you can start reviewing others' work or maybe even get responsibilities over areas, particular services or topics.