The significance of the Git version control system lies in its ability to manage and track changes in software development projects. Git allows multiple developers to collaboratively work on code, facilitating features like branching and merging, which help in maintaining project organization. It enables teams to revert to previous versions, resolve conflicts, and maintain a comprehensive history of changes made within a repository. This capability not only enhances collaboration but also fosters accountability, streamlining the software development process and improving overall project management.