Tax liability, in financial terms, is the total amount of tax you owe before subtracting prepayments or withholdings. "Liability," at its root meaning, is similar to "responsibility," so think of your tax liability as the money you are responsible for paying to the government. On a W-4, the section on "Tax liability" is used to determine whether or not you are exempt from tax withholdings on your earnings.
Form W-4
Form W-4 tells your employer how much to withhold from your paychecks to cover federal income tax payments. Form W-4 line 7 lists two conditions for claiming yourself exempt from having taxes withheld from your pay: you had no tax liability the previous year and you expect to have no tax liability for the current year.
Prior Year Liability
In rare cases, you may be entitled to have all taxes withheld from your paycheck refunded to you because your personal income tax calculations showed that you did not owe that money after all. If you were refunded the entire amount withheld on your prior year's taxes and did not owe any taxes for any other reason, then you had no tax liability for that year. However, if you simply did not owe taxes on your tax return, this does not mean you had no tax liability. It means the taxes you were responsible for paying were already withheld, and you are still subject to tax withholding.
Current Year Liability
Claiming exemption on your W-4 allows you to receive more money from each paycheck because the federal income taxes are not withheld. If your income situation has not changed at all since the prior year, and you had no tax liability for that year, you will most likely have no current-year tax liability. In this case, claiming exemption puts money in your pocket throughout the year rather than receiving it as a refund after you file your taxes. However, if you miscalculated or your situation changes during the year, you may end up owing taxes plus penalties for not paying those taxes throughout the year.
Considerations
Depending on your work industry and environment, it can be hard to predict what your income status will be throughout the course of the year. When determining whether or not you expect to have tax liability for the current year to complete your W-4, look at the overall stability of your financial situation. If you expect any changes in employment or deductions, do not assume you will have no tax liability for the year; instead, fill in the W-4 without claiming exemption from withholding.