Those rights were the previously mentioned unalienable rights and others not specified.
The Founders meant that the only legitimate powers of government involve protection of our God given, unalienable, Natural Law rights.
The Constitution itself codified this belief on the nature of legitimate government power.
Think about it. The powers granted by the States to the new federal government were consistent with Natural Law, the Law of our Creator.
How far we have fallen since our rejection of Natural Law and the embrace of Marx.
Whenever anyone talks about “life, liberty and pursuit of happiness” I like to continue the quote with the line “to secure these rights, Governments are instituted among Men, deriving their just Powers from the consent of the governed” and the line “whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government.”
The looks on their faces tells me everything I need to know about what they believe this document meant in 1776 and what it means today.