The roots of this formation are more than likely to be found with the velites, the lightly armed skirmishers who operated ahead of the main force in the early Roman army.
The wide spaces allow each soldier great mobility. Its possible uses were manyfold.
It would make an advance over difficult terrain much easier. It could allow for swift attacks with subsequent quick withdrawals. It would allow for any friendly units falling back to pass through the formation.
It also could be used by a victorious army sweeping over the battle field, killing all that was left in its way.