What you are asking about here is the third element in the usual plot diagram of a well-written story: exposition, inciting incident, rising action, climax, falling action, resolution. In The Slave Dancer the rising action consists of all the events that happen after Jessie Bollier is kidnapped. Why? Because the kidnapping is the "incident" of the plot; therefore, everything after that incident and before the climax makes up the rising action.
Everything in the rising action has to do with the workings of Jessie Bollier as the "slave dancer" on a slave ship. In other words, he is the boy who plays the music for the slaves to "dance," which is just a fancy way of forcing the slaves up onto the deck to give them some exercise, sunshine, and cleaning. Jessie is disgusted by his "job." He hates it and finds slavery inhumane.
I hated what I did [playing the fife]. I tried to comfort myself with the thought that, at least, it gave them time out of the hold. But what was the point of that or anything else?
These thoughts and others are all part of the rising action. Most of this is the doings of the slave ship Moonlight and the horrible treatment by the captain and other shipmates. When Ras (a slave) and Jessie (the cabin boy) survive both an attack and a shipwreck, that ends the rising action for THAT is the climax! Everything else from there is falling action and resolution.
As you can see, the rising action is one part of the plot that often has many elements and often has a lot to do with suspense. This is because it leads to the climax of the story, in this case, the novel The Slave Dancer.