Q. I'm wondering if I will have to pay both state income tax in NY and MS?
A. Yes, most likely. You will (most likely) be considered as working in NY, under the convenience of the employer rule, and your wages taxed by NY. But, MS will give you a credit. or partial credit for what you pay NY, so there will be little or no double tax.
Q. I read New York specifically has something called the Convenience rule for telework, but I'm having trouble understanding.
A. Why are you working in MS, instead of NY. If the job could be done in either place, then you working there for your convenience and are subject to NY (the employer's location) tax. If you need to be in MS as a job requirement (meet customers, supervise employees, stock shelves etc etc), the you are there for the employer's convenience and subject only to MS tax.
If you work outside the state as a job requirement, you are only subject to New York State income tax on the days you work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your income. Pennsylvania, Nebraska, Delaware and New Jersey have the same rule. For guidance see: http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
Here's a link to New York's memorandum on its "convenience of the employer" tax doctrine regarding non-resident telecommuters: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
