It's so abundantly simple that it shouldn't need explaining, but the Adam Smith Institute hasn't done a bad job:
"The error is in seeing the government as being external to the economy, with spending coming as manna from heaven. In fact, government money does not come from nowhere – barring simply printing money to pay for spending (which obviously does not increase actual wealth), government spending money can either come from taxes or borrowing."
Anyone can see that taking it from taxes is a transfer from the private sector to the state, and simple redistribution. If this generated wealth, then North Korea would be beating South Korea.
How about borrowing though? Surely that's bringing money in?
"Government borrowing comes from private savings, crowding out private borrowers like entrepreneurs and investors. By diverting money away from businesses and entrepreneurs, who can use it to create commercially-valuable projects, wealth is squandered on projects that are unproductive such that only a government. If they were productive, why would it be necessary to tax people to pay for them in the first place?"
Now some make the argument that governments can make productive investment, in certain infrastructure where the private sector is prohibited or crowded out. This can be true if the projects selected are high value, but this is only a second best option and only reflects the failure to allow market signals to incentivise the private sector to enter such markets (the best example is with roads).
Yet neither in the UK, nor in the US (nor New Zealand) is such deficit spending about roads, it is about consumption.
This is why eliminating deficit spending is positive for economies. It gets the government out of competing with private businesses for borrowing (of all sizes), so it reduces the cost of borrowing. As government debt is typically seen as one of the safest "investments" (nothing like lending to someone who can extract repayment by force from its subjects), reducing the supply of such debt will induce financial institutions to look elsewhere for returns.
After all, Japan has been deficit spending now for over a decade, and the results have remained lacklustre.