If the state of Mississippi wins the case, depending on the nature of the justices’ ruling, it could effectively end the Constitutional right to abortion and pass the job of regulation over to the states, many of which are prepared to immediately limit when, how and where abortions can happen.
Roe v. Wade and Planned Parenthood v. Casey, which — among other things — does not allow bans on abortion before a fetus is viable (usually around 24 weeks).
Fundamentally, Mississippi's argument is that overturning Roe or Casey is not a ban on abortions, but a way to allow Americans to resolve the question on their own through the democratic process, state by state.