Explain a long train of abuses and usurpations?

Abuses: things which are used wrongly

Usurpations: occasions when someone usurped someone else's authority or privileges. Usurped means took away wrongly (a kind of stealing which only applies to authority, privileges, or titles)

"A long train" is a metaphor. Like a train, the abuses and usurpations are hitched one after the other in a long series.

The person might be talking about a supervisor at work. "On Monday, she locked the staff bathroom, which she had no right to do. On Tuesday, she ate her lunch in the red room, which is Jodi's room. On Wednesday, she told Jodi she had to use her own stationery, which is totally wrong. On Thursday, she told Jim that he could not welcome the Chinese visitors as he was planning to do, because she was going to do it. It's been a long train of abuses and usurpations."