According to The Declaration of Independence for Dummies, Part 1,
”But when a long train of abuses and usurpations, pursuing invariably the same object, evinces a design to reduce them under absolute despotism, it is their Right, it is their Duty, to throw off such government, and to provide new guards for their future security.”
can be reworded "in street corner English, as
But when a government becomes tyrannical and abusive with consistent, repeated violations of the people’s rights, with the intent to make them slaves of the state, then the people have the right–in fact, the duty to revolt against the government, and put new rules in place to protect their future rights.
I happen to think this is an acceptable 'dumbing down' of the Declaration.
As you can see by this interpretation, "a long train" has nothing to do with a railroad train, but more of a long history of violations of the Rights of Man. The writers of the Declaration were telling the World Powers, and their own people, that over the millennium, Kings, Emperors, and other despots trampled on these Rights and that the "long train of events" culminating in the imposition of taxation (of the Colonies) that was enacted to help pay off the recent war by England. The Subjects who were facing this taxation never were afforded the opportunity to raise their own voices in Parliament, as would Subjects at home.
So the writers were, in essence, saying that over the course of history, many rulers had trampled on the Rights that were being declared here, and enough! we weren't going to take it any more.