The BIM levels depict maturity levels.
BIM Level 0 - Low collaboration
This level of Building Information Modeling only includes 2D drawings using CAD (Computer Aided Design). Participants only share files, documents, drawings etc. via electronic prints and paper. There is no collaboration.
BIM Level 1 - Partial collaboration
It is not only about 2D drawings here, but 3-dimensional views are also considered. In level 1 BIM, teams are sharing information using a Common Data Environment (CDE) (such as Bimsync). That allows them to collaborate easily on projects.
Nevertheless, there is still no collaboration (or low collaboration) between different disciplines, still each one owns its data and does not share it.
BIM Level 2 - Full collaboration
All participants are using their own 3D CAD models, but not necessarily working on a single, shared model. Collaboration occurs between different disciplines, by using a common file format i.e., IFC (Industry Foundation Class). IFC allows project's actors to access the data so everyone is able to work on the model.
BIM Level 3 - Full Integration
The level 3 of BIM is about full collaboration, that means every discipline collaborates through the same shared project. It includes 4D (construction sequencing), 5D (cost), and 6D (project lifecycle information). Everyone can access the data, and edit it. This is what we call Open BIM. See article: 5 good reasons to use Open BIM.
BIM Level 4 - To go further
Level 4 has been introduced recently and includes social outcomes.
Related term: IFC, BIM dimensions