EMP
An electromagnetic pulse generator (EMP) is an anti-electronics weapon that mimics the intense EM radiation emitted by a nuclear explosion in an atmosphere. The resulting EM field couples with nearby electronics systems, inducing massive, damaging electrical currents.
Just before the Cylon attack, "electric pulse generators" were being transported to Caprica from Battlestar Galactica on Colonial Heavy 798 (later Colonial One), presumably to place in a planet side museum or school as a historical artifact, or for re-use on another ship (Miniseries).
As the destruction of the ship by a Cylon raid was imminent from nuclear missiles, Lee Adama activated the devices, giving the appearance that Colonial One had been destroyed by a nuclear blast. This attempt was successful, as the Cylons cut off the assault, the missiles were disabled, and Galactica's Dradis confirmed the ship as destroyed. Colonial One's electronic systems seemed to be fully functional after the attack.
It is probable that these devices are standard equipment aboard ships such as battlestars, given Lee Adama's knowledge about the electric pulse generators. It is also probable that such devices were part of a battlestar's fighting tactics against Cylon attacks, since (at least in the first Cylon War, although not in the second), Cylons were purely mechanical and thus vulnerable to EMP attacks unless shielded from the effect. Given that a non-military craft such as Colonial One recovered very shortly after the pulse, even Colonial civilian vessels seem to be equipped with EMP-shielded electronics.
During the Fall of the Scorpian Fleet Shipyards Pegasus gained valuable time to escape with a blind jump when the radiation - not a magnetic pulse as those aren't created in space - from the Cylons' nuclear weapons temporarily blinded their own Dradis.
In the Miniseries the EMP is shown to temporarily overload the crew's central nervous system. However, this is scientifically incorrect, since electromagnetic pulses are extremely short in duration. Moreover, while the human nervous system works with electrical currents, there is no metal to act as antenna for the magnetic field and induce a damaging current. The effects shown are either a writing error, or the result of some other force.