1) Form a more perfect Union
It means that they wanted were joining up all the colonies and they were getting together to form a single country. So it speaks of a union because they are joining together as a nation separated from Great Britain.
2) Establish Justice
It refers to the law. Establishing justice is very abstract and it means creating the legal system with their own laws to ensure justice and fairness for the population.
3) Insure domestic Tranquility
Guarantee public peace and safety after many revolts and disputes within the states.
4) Provide for the Common Defense
It means to defend the country against foreign intervention. It is making reference to military defense. So the states won't have to defend themselves all alone, the whole nation would be in charge of that from then on.
5) Promote the General Welfare
It reinforces the idea of the government having some responsibility to the social wellbeing of its citizens and providing essential things such as healthcare and education.
6) Secure the blessings of liberty to ourselves and our posterity
Its goal is to preserve the liberty for everyone and future generations. The U.S was a nation founded on liberty and justice, and these inalienable rights must be preserved in order to remain great.