Why were the Ninth and Tenth Amendments put in?

That is a great question!  We can look at the language of the amendments to determine their purpose.

Here is the Ninth Amendment:

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

What this means is that the Constitution and the previous amendments could not possibly "list" all the possible rights that people might have, so if there were/are other rights we have...

That is a great question!  We can look at the language of the amendments to determine their purpose.

Here is the Ninth Amendment:

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

What this means is that the Constitution and the previous amendments could not possibly "list" all the possible rights that people might have, so if there were/are other rights we have had that might be challenged, this amendment says that no one can try to take them away or discourage us from asserting them.  If you think about this for a minute, it makes a great deal of sense, since the founding fathers could not think of everything as they put together this amazing document.  There have been rights not mentioned outright in the Constitution that have been upheld, for example, the right to privacy. 

The Tenth Amendment is extremely important. Let's look at it:

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 amendment is meant to address the tension of power between state governments and the federal government.  This tension existed from the very beginning, with states being concerned about the power of the federal government, and it exists to this day.  This amendment protects the rights of states to legislate and regulate in any area that is not specifically mentioned in the Constitution.  This explains, for example, why family law, most crimes, and commerce within a state are regulated by state governments, not by the federal government. The powers that the federal government has are called the enumerated powers, meaning those set forth in a list.  If something is not on the list, the federal government may not control it at all.  People who are strong states' rights advocates point to this amendment to argue that the federal government is sometimes trying to overreach its powers.