What does the following text mean: That to secure these rights, Governments are instituted among Men, deriving their just powers from the...

This passage is from the Declaration of Independence which was written by Thomas Jefferson.  It was signed on July 4, 1776.  I am not sure what your question was, so I will dissect the different parts and give an explanation for each section.  The Declaration of Independence was the means by which the colonists communicated the rationale for dissolving their relationship with England.  

...That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed... 

This excerpt communicates the colonists belief in popular sovereignty and the idea that governments are formed by people to serve the needs and interests of the people.  In other words, since the citizens create the government, the government is created in their interest.  

...That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it...

This concept from the Enlightenment period is the idea that people have the right and responsibility to replace a government that is tyrannical and oppressive.  The Declaration of Independence also lists the various grievances the colonists held against England.  These grievances form the justification for separation.

and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness

This portion is rather obvious in that if you destroy one system of government, it is necessary to replace it with another form.  This also speaks to the idea of a government that is responsive to the needs of the people.