If you do not provide your TIN to your client, they are supposed to withhold 31% of your payment as tax withholding. The withheld amount would be submitted to the IRS as "Federal income tax withheld". They would then report the gross amount and withheld amount on a 1099 form. For example, "Nonemployee compensation" would be reported in Box 7 of the 1099-MISC Miscellaneous Income form. Any withheld amount would be reported in Box 4 ("Federal income tax withheld"). You'd report all this on your income tax return.
If you do provide your TIN, your client will not be required to withhold 31% and you would be paid the full amount. You will still receive a 1099 form, but you'd be responsible for submitting estimated taxes to the IRS instead of your client.