What does that mean for people who don't know what the amendments are?
I'm sure that you know that the US Constitution is the highest law, so everything we do must be in line with the intent of the text (not the interpretation of the text, as some politicians like to think).
The 10th Amendment reads: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people."
This means that if the Constitution doesn't specifically give power to the Federal government on an issue, the States are responsible for that issue. All 50 states have the authority to handle these issues as they see fit, and can handle them in 50 different ways if each state so chooses.
The 14th Amendment is a long one, but the passage of Section 1 applied in this case states: "... No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States... nor deny to any person within its jurisdiction the equal protection of the laws."
The Supreme Court ruled that this passage of the 14th trumped the 10th in this case. This logic, now written as Case Law, can be legally applied in future cases where any person feels that a State's law denies them equal protection and can override State law.
It will be interesting to see how this case law is applied in the future.