All of your income is subject to tax by the state that you live in, no matter where the income is from. Income you earn for working in a particular state is subject to tax by that state, no matter where you live. So when you live in one state and work in a different state, the money you earn is subject to tax by both states. But, as xmasbaby0 said, the state that you live in gives you credit for part or all of the tax you pay to the state that you work in.
The tax that you paid to Louisiana is not credited to Mississippi automatically. To get the credit you have to file tax returns in both states: a nonresident tax return for Louisiana and a resident tax return for Mississippi. On your Mississippi resident tax return you get credit for part or all of the tax that you pay to Louisiana.
Depending on the relative tax rates of the two states, and whether you have any other income besides the job in Louisiana, the credit might not completely eliminate any Mississippi tax. Mississippi knows that you had income from working. If you did not file a tax return in both states, Mississippi does not know that you paid tax to Louisiana, so they may think that you owe Mississippi tax on your entire income.
Some states have special arrangements that are exceptions to these rules, but there are no exceptions for Mississippi or Louisiana.
