A success roll is a die roll used to "test" a trait or skill of your character. As you know, each skill a character has will have a single die associated with it. To test that skill, roll the die. If the roll is a 6 or less, you have succeeded. If roll is greater than a 6, you have failed. The lower the roll the more complete the success, or the higher the roll the more dismal the failure.
As you may notice, that means that a Grandmaster will never fail a normal test, and an average person will fail about half the time. (Well, that makes sense, doesn't it?)
However, sometimes the "target number" will be set differently than a 6 by the Storyteller. For particularly difficult tasks, the target may be a 2 or a 3. There are no charts for this or even guidelines. It's all up to the Storyteller and the influence of the Three Precepts.
For speed of play, always assume that the target is a 6 unless the Storyteller specifically says otherwise. Success rolls (or any other type of roll, for that matter) should only be made when the Storyteller asks for it. Most of the time, the course of the story can be determined narratively, by you and the Storyteller. Dice are only a tool to help guide the action when you can't decide whether success or failure would be better for the flow of the plot, or when an element of chance makes sense or adds to the fun.
The metal catwalk before Ryla's path was slick with rain, gleaming in the torchlight. The Ogrean battle cries continued to grow bolder as the others struggled to hold back the surrounding enemy.
"Move, by god!" Commanded Laerd. Ryla was terrified, but the catwalk was the only way out. With a prayer and a gasp, she teetered out over the chasm.
The Storyteller interrupted the narrative. "Ryla, make an agility roll, target of 4." Ryla was no athlete. Her agility was average at best. (D12) She tossed the die... a 3. All she needed was a 4 or less: she made it.
Laerd watched breathlessly as Ryla's torch swayed its way across the catwalk, her feet struggling to find purchase on the slick metal. She reached the other side and turned to look back, motioning frantically for the others to follow. The Ogrean began to charge...
"I'm going to disengage and run across as fast as I can," decided Laerd.
"That's not so easy, Laerd," warned the Storyteller. "Make an agility save, target of 3." Laerd was a warrior, and he had great balance (D8). He spun and dashed across the beam. The die was tossed: a 7.
"Aye!!" Laerd's foot came out from under him. Ryla screamed as she watched him fall and splash into the freezing water below... He hit hard, and was swallowed into the rush.
"Make a health save, Laerd" said the Storyteller ominously, "and you better not miss this one..."