The six goals stated in the Preamble of the U.S. Constitution are to create a more unified government that upholds justice, peace, defends and advocates for the health and prosperity of its people, and protects human rights and freedom.
"To form a more perfect Union" meant creating a better government than the British colonial rule. The colonies had no representation on any level of government beyond the local ones. This first goal stated in the Constitution was to establish a federal government that worked in union with its people and local/state governments.
To "establish justice" refers to the goal of making a fair justice system. One of the key principles of the revolution was equality, and a fair judicial system is a key part of that.
The goal of "[insuring] domestic tranquility" is to keep the peace within the country's borders. This means keeping citizens happy with their government, avoiding the kinds of turmoil that led the founding fathers to writing the Constitution.
Along those lines, the next goal is to "provide for the common defense." This is the step up from simply avoiding turmoil; it is defending the country against any threats that may arise.
"[Promoting] the general Welfare" is the goal of establishing a government that cares about its people. Examples of this goal being carried out are the food stamp programs, Section 8 housing making sure low-income families have somewhere to live, as well as the Food and Drug Administration, or FDA, regulating the food and medication sold in the country.
The last goal of the preamble is to "secure the Blessings of Liberty to ourselves and our Posterity," meaning to protect the freedoms that the revolution fought for. "To ourselves and our Posterity" refers to keeping those freedoms alive for future generations as well.