A glitcher can work in a number of ways, the main ones being a clock glitch or a power glitch.
Normally, on a smartcard the clock is a steady frequency (usually between 2.5Mhz and 5Mhz) with an approx 50% duty cycle (high-lo period). A glitch disturbs this clock by inserting a relatively quick pulse (usually at least 5x, often a lot more, the speed of the clock) the idea being to cause corruption to some aspect of the smartcard processors operation.
The power glitch works in a similar way but instead of inserting extra clock pulses the power line (normally a steady voltage) is very quickly removed (or reduced or possibly even increased) and re-applied. Again, the intention being to cause corruption or mis-operation within the smartcard.
Corruption in the processor can take many forms, some possibilities being -
1/ The corruption of the program counter so execution continues from some other program address.
2/ Interfering with an instruction load or decode so the processor see's a different instruction from the one originally intended.
3/ The corruption of processor register contents
4/ The corruption of RAM contents
There are also many other forms of corruption that can cause processor malfunction but the general idea is to corrupt things in such a way that it does things that are beneficial to us - perhaps something like skipping a password check or maybe running some rogue code that has been inserted previously !