|The blockchain records all the transfers of money. If you have only 1 ZEN, and create two transactions at the same time, attempting to spend the same coin twice, the network needs to agree on which of the two transactions was first, and therefore, valid.|
The consensus mechanism ensures that the entire network agrees on the order of transactions. There are different ways to come to a consensus in a peer-to-peer network. On the Horizen blockchain, people vote with their computational power on the order of transactions. If your computer is twice as fast as mine then the chance of you deciding on the order of transactions is twice as high as me deciding on it.