The significance of Git in software version control lies in its ability to track changes in source code over time, enabling multiple developers to collaborate efficiently. With Git, developers can create branches to work on features independently and later merge their changes back to the main codebase. This helps prevent conflicts and maintains a history of all modifications, facilitating easier debugging and code review. Git's distributed nature allows every developer to have a complete copy of the repository, ensuring reliability and access even without an internet connection.