Traditional IRA basis is the funds in an IRA that already have been taxed, either as nondeductible IRA contributions or after-tax funds rolled over from plans.
Roth IRA contributions and Roth conversions are all basis since those funds have already been taxed.
Tracking IRA basis is necessary to determine the taxation of eventual IRA withdrawals. If basis is not taken into account, tax-free withdrawals can become taxable, meaning the funds will be taxed twice.