Why was the power to veto laws signifacant?

Answer 1

It is but one significant step in the process of protecting the rights of the people. In their zeal Congress has and will continue to invent laws that speak to popular concerns. If these laws abrogate or derogate the rights of the individual, then the President has no other authority but to veto. If the legislative body is able to pass the legislation after this, it is then up to the courts to protect the rights of the people. But at all times, it is up the individual to assert their rights when being encroached upon.

Answer 2

Only the plebeian tribunes had the power to veto a law during the Roman Republic. They were the representatives of the plebeians who were established during the first plebeian rebellion (the First Plebeian Secession, 494 BC) which started the Conflict of the Orders between patricians and plebeians. In the negotiations to end the rebellion, the patrician-controlled senate agreed to recognise the plebeian tribunes as the leaders of the plebeian movement and grant them the power to appeal against any actions by officers of state they deemed as being against the interests of the plebeians and the power to veto laws.

The officers of state also had the power to veto, but this was related only to the actions of other offices. Officers of the same rank could veto each other's actions and officers of higher rank could veto the actions of officers of lower rank. This was part of a system of checks and balances