So... its kind of a mouth full but makes sense in the end.
The American Revolution pretty much created the united states and influenced the preamble and the constitution. the framers wanted to secure their blessings of liberty, this liberty being their new government constitution. So, the original meaning behind secure the blessings of liberty was to fulfill the goals of the preamble and the constitution. But then throughout time it began to mean something kind of different, society began understanding this section as securing your rights (which makes sense but not 100% accurate) and as the responsibility to bring justice. Civil Rights Act of 1964 = securing the blessing of liberty. Why? because it brought justice.
Another difference is that now this section also refers to fixing past generations mistakes. Even though the section contains "to ourselves and our prosperity" for some reason many generations had difficulty securing the liberty to the next generation and that led to some really bad things like slavery and some not so bad things but still sucky things like poverty.
So yeah. Securing blessing of liberty = secure the preamble and constitution.
preamble and constitution = the blessing of liberty