What does it mean to make a "pre-tax" contribution? What does the tax payer need to do when filing their income tax return?

All employer money is contributed to HSAs without having income taxes/employment taxes withheld. Additionally, most employers allow their employees to reduce their salary by the amount they want the employer to send directly to their HSA before income taxes or employment taxes are calculated (see Are HSAs allowed under a Section 125 Cafeteria Plan for more information). The employer forwards the funds on to the HSA directly on a pre-tax basis. The employer reports all pre-tax HSA contributions on the employee’s W-2. When the taxpayer calculates their eligible deduction, these contributions are not included because no income tax was ever paid on these contributions.