The eurozone countries hope that using the same money will make it easier to buy and sell things to each other.
They won't have to convert between different currencies.
For example, if you want to buy something in the USA and you live in Britain, you have to convert your pounds into dollars.
This costs a lot of time and money - particularly for businesses.
Also, the amount of dollars you get might change, which makes it hard for businesses to work out how much money they've got.
In theory, life is much easier and more simple with the euro.