A right of veto means that somebody can stop decisions or legislation.
For example, the President of the United States has veto power over the USA's Congress. This can stop legislation from being passed.
Similarly, the five permanent members of the United Nations Security Council (The United States of America, the United Kingdom, China, Russia and France) each has veto power. Using this, they can stop the security council's decisions from being passed and becoming resolutions.
The veto was invented for the Roman tribunes so they could protect the people from bad laws made by the Roman Senate.