If you are asking about filing a tax return, social security is not taxable income if it is a person's only income, but it may be taxable if the person has other income like investments or a pension. How much social security is taxable depends on a complicated formula and the best way to figure it out is to use the IRS calculator or to actually prepare a tax return and see what the answer is.
https://www.irs.gov/help/ita/do-i-need-to-file-a-tax-return
https://www.irs.gov/help/ita/are-my-social-security-or-railroad-retirement-tier-i-benefits-taxable
If you are asking about claiming someone as a dependent, social security is "support" they provide themselves (even if it is not taxable), and does count when you are trying to figure out if someone else paid more than half the person's total financial support.
Regardless of whether or not social security is taxable for a particular person, it is not "compensation" or "earned income" for tax purposes that require that type of income, such as certain credits or making IRA contributions.
