Governments levy taxes to raise revenue for public projects. Taxes discourage market activity. When a good is taxed, the quantity sold is reduced.
However, the question is: when a tax is levied, who bears the burden of the tax?
Tax incidence studies this. A tax on the sellers shifts the supply curve (to the left) and a tax on the buyers shifts the demand curve (to the left). In the longer run, taxing the sellers results in the price of the good increasing and taxing the buyers results in the price of the good decreasing (but the price of the good plus the tax increases). This allows us to analyze how the equilibrium changes.
It should be noted that regardless, buyers end up paying more and sellers receive less. So no matter how the tax is levied, the buyers and sellers share the burden, either directly or indirectly. The two taxes are equivalent!
For a payroll tax, the difference between the wage the firm pays and what the worker receives is called the tax wedge, which is just the volume of the tax that goes to the government.
The burden usually ends up being heavier on the side of the market that is less elastic. Indeed, a small elasticity means that the people don’t really have any alternatives, so they stick with the good even if it is actually a bad.
So for a payroll tax, the workers bear most of the burden, not the firms.