How does consumers spending money boost the economy?

The level of economic activity in a country can be measured by the amount that is being spent on goods and services, wages and salaries, construction and infrastructure, military and other security activity, net sales of exports; and so on. This measure is usually called National Income and sometimes Gross Domestic Product [GDP.]

By definition, GDP comprises the following, with typical figures for USA over the past 25 years:

Consumer spending [65%]
Industrial spending [15%]
Government spending [8%]
Foreigners spending on our goods and services but also minus our spending on foreign goods and services [12%]

So consumer spending is the major source of economic activity [work], wages and salaries, purchase of goods and services, taxes to pay for government spending [military, space exploration, medical research etc.]

Boosting the economy requires that consumer spending should be maintained by any means possible.
In fiscal policy, this means reducing tax rates, greater government spending on benefits and entitlements [by borrowing of course, since tax revenues will fall], and by spending on big structural projects [roads, dams, drainage and water supply, flood prevention, etc.]

In monetary policy, it means reducing the cost of borrowing [interest rates] and freeing up sources of credit through banks and other financial intermediaries.

Unfortunately, in USA today, only the second of these is being managed. As if the interest rate, by itself, will bring the economy back into balance. Impossible; but the Fed and the Washington administration don't seem to want consumers to contribute to economic recovery.
So we have a long period of austerity.
Totally the opposite of what is required.

Increased spending on goods and services will increase demand. This will stimulate production and this will require people to be hired, who in turn spend money.

If he/she has broken the window for example, it will increase spending. The guy who can fix the window will get the money, but has to pay for the glass factory, and so on. All round and round, it will stop somewhere, and the total income will increase x times more than the spending. X is found by Keynes who called it multiplier.

It sets the wheels in motion