The signals moving between the smartcard and the receiver can be
easily intercepted and analyzed. They can be vulnerable to a "glitch"
by which the incoming power and clock signals are disrupted for a
short and carefully timed length of time (such as a millionth of a
second) in order to cause the processor to skip an instruction. In
many cases, off-the-shelf hardware with modified firmware designed to
exploit this weakness was sold to pirates for use in tampering with
cards for the US-based DirecTV system.
Short answer: a program running on a processor can be manipulated by introducing a glitch in the power supply. Processors are made up of transistors, each instruction has transistors dedicated to it. If you are familiar with assembly there are instructions to add, subtract, multiply, store/load and instructions to control program flow, like jump and compare. The hackers are analyzing a program on a processor, at a certain point in the program (maybe they want it to jump to a different instruction, or add some numbers together wrong) they introduce a glitch in the power supply\clock to change the state of the transistors and cause an intentional error in the program to change the way the program runs on the processor. You would have to do a lot of experimentation to get this to work right.