Recovered from the collection of alien fanatic Henry Parker, the Pulse resembles a glowing red-and-black meteor or "radioactive conch shell" in its dormant state.
Parker named it and believed it to be a healing device and the only thing that kept him alive despite his ill health. It was not a healing device, but, as Owen Harper later learnt, it was actually a message sent by a race who had received one of Earth's past transmitted attempts in the seventies to discover proof of extra-terrestrial life, containing a message that is somehow 'displayed' through a brilliant light show that is generated by the Pulse when it reaches full power.
The Pulse started to leak dangerous radiation during its intial activation in Parker's home, and Torchwood stepped in, infiltrating his house and neutralising the device.
Unfortunately, Mr. Parker died of a heart-attack moments after his conversation about the Pulse with Owen Harper, who was unable to revive him because he no longer breathes and was therefore unable to perform CPR. (TW: A Day in the Death)
The Pulse is pressumably somewhere inside the Torchwood vaults.