The term "absolute despotism" refers to the actions of a government that is failing to protect the rights of citizens. This type of government is extremely controlling and does not consider the rights/needs of the individual. This is evident from the sentence that this phrase is used in, as the Declaration of Independence states that
"But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism,..."
This line shows that this is a direct reference to the abuses of government power over their respective citizens.