Paying an employee under the table means that they pay you in cash instead of a direct deposit or paycheck which means it saves the employer having to deal with taxes and payroll paperwork.
It saves the employer money and time by not having to pay their employees through paychecks or direct deposits.
But if the employer does pay you under the table then you won't usually get a W 2 Form and then the money you earned won't be taxed.
That seems like a good thing but the income taxes you pay in comes back to you eventually through a social security check once you reach retirement age.
So it's best to pay your income taxes because not only is it the law it's gonna hurt you in the long run unless you have a lot of savings in the bank for retirement.
I've had a few employers pay me under the table at part time jobs and that was okay for me but if I was full time I would want a paycheck or direct deposit so I could easily report the income to the IRS.
Doing payroll includes having to figure out things like figuring out tax reductions, keeping records, reporting employee's income, etc and so on so it saves a lot of work and headache for the employer to pay under the table in cash.