This is potentially a very complicated area.
Here's the simple situation: They basically give you a raise, with the plan that you use it to buy personal insurance on the marketplace. The income is taxable, is included in your W-2 as taxable wages. Assuming you do buy insurance, the fact that you are paying with taxable funds means you qualify for the ACA premium tax credit (depending on income) and/or the itemized deduction for medical expenses.
Here's a situation that gets very problematic: The business establishes an HRA, health reimbursement arrangement. This is a fund for your medical expenses that is contributed to only by the employer; employees are not allowed to contribute. The employer can reimburse your out of pocket medical expenses that you prove with receipts. The reimbursements are tax-free to you and a business expense to the employer. The employer funds the HRA with a set amount per year. Unspent amounts can be rolled over to the next year, or returned to company funds, but can't be paid to the employee.
Now, before the ACA ("Obamacare"), it was legal for companies to use an HRA to reimburse employees who bought their own medical insurance. This saved small companies the hassle of buying a small group plan, and allowed the employees to save money by buying their insurance with tax-free dollars. Under the ACA, this is now illegal, and the fine for noncompliance is $100 per day per employee.
Employers now have two options that are legal. They can provide you with employer-sponsored group health insurance that is ACA compliant, and then also offer an HRA to reimburse you tax-free for out of pocket costs like co-pays. Or, if they have fewer than 25 employees and are exempt from the ACA employer mandate, they can provide you with taxable money to buy your own insurance, and it's simply treated like a raise in pay.
If your employer thinks they can reimburse you to buy your own private insurance and have it be tax-free, they need to talk to an accountant or health care specialist immediately, because it's illegal and the fines are brutal.
