Bob the Archer wants to shoot something with his bow. He has 4 reflexes (Relevant Stat) and a ranking of 3 in Kyujutsu (Archery)
Thus he rolls 7 dice and gets to keep 4 of them. The DM determines it to be a tough shot with a Target Number of 25.
Bob rolls his seven dice, he gets 2,10,2,5,9,8,6. He picks 4 from this pool and given that he wants to succeed he chooses the 10, 9, 8 and 6, giving him a total of 33, easily succeeding, but wait the 10 explodes and he rolls another d10, it's a 4 bringing him up to 37 which is still just a success. If you want to get more than a normal success you have to buy raises and hope that you don't fail.
For example, Jimmy the Courtier wants to see if he can if someone is lying. The DM adjucates that the TN is only 10, but Jimmy wants to know more than if he is simply lying or not, he wants to get a glimpse into perhaps why he is lying, so he buys two raises bringing the TN up to 20, remember if Jimmy fails this he won't get anything out of it. With his Awareness of 3 and his Ettiquette of 2 he decides to go for it anyway, rolling 5 dice in total (3+2) and keeping 3 of them. Jimmy gets 9,7,5,3 and 2. He keeps the 9,7 and 5 for a total of 21, a success and he learns the other guy seems to be lying to protect someone. If instead of a 9 he had rolled another 5 his total would have been 17 and despite it beating the original TN he would still fail.