What is state withholding? Instructions read: "Maryland only requires a 1099-MISC from the payee (or employer) when there is Maryland withholding greater than zero."

State withholding is when the taxes for Maryland have been taken out ahead of time and reported on the tax document.  Withheld tax is common with wages paid on Form W-2, but it is very rare when the individual is paid as a contractor on Form 1099-MISC.  If the company or individual who contracted you did not withhold any Maryland tax from your income (and they probably did not), then, if you are mailing in your Maryland return, you do not need to include the 1099-MISC along with your tax return when you mail it in.  

Thank you very much, Daniel. I am the payer in this case, I have electronically filed this payment on TurboTax Quick Employer Forms to the IRS. Do I have to mail or submit anything to the State of Maryland?

If you did not withhold any Maryland tax, then no.  The subcontractor will use the information on the copy you provide him to file Federal and Maryland tax, but Maryland will not need a copy of the 1099-MISC if tax was not withheld.