Not much is known about Pulse's background. He's been a cat burglar, breaking into people's home to steal art, for many years. During that time, he'd met and remained acquainted with Mystique.
Pulse was created by Peter Milligan and Salvador Larroca and first appeared (obscured) in X-Men #173. His first full appearance was in X-Men #179.
Major Story Arcs
Pulsing the X-Men
Initially, Pulse was a mystery figure hidden in shadow. While she was disguised as Foxx, he was a contact for Mystique whom she called for more psychic buffering that would help hide her true identity from the X-Men. At that point, all we knew of his character was that he was a skilled art thief who recklessly left his cel phone switched on while breaking into populated residences.
Information about Pulse
It was some time later before any information was revealed about Pulse, including his name & appearance (as he'd only been seen covered from head-to-toe in black). His character wasn't given much room for development, as he'd been introduced purely as a romantic wedge to drive between Rogue & Gambit. Pulse's own mutant ability meant that it was possible for Rogue to physically touch him. His arrival came at a time when Mystique (disguised as Foxx) had already been trying to seduce Gambit in an effort to destroy his relationship with her daughter. By introducing someone who could physically touch Rogue, Mystique was sure that she could remove Gambit from the picture. Therefore, as he was just someone who was introduced because of his powers, Pulse wasn't given much opportunity to develop his personality.
Pulse wasn't a team player, and repeatedly emphasized that he was a self-serving coward. He didn't like combat situations. However, he managed to overcome his innate cowardice to nullify Apocalypse in battle long enough for the X-Men to defeat the External in battle, and later on he managed to confront Death (Gambit, who had been transformed into the Horseman) who was trying to kill Rogue.
Feelings for Rogue
Despite having never met Rogue before, Pulse seemed to be easily manipulated into a relationship with her. He was led to the X-Men by Mystique, despite having a personality that goes against the natural adventurous nature of the team. However, after some time he did manage to express his own romantic intentions towards Rogue. However, he was instantly rebuffed which was the last time he was seen. Therefore depriving him of any chance to further progress his personality.
Powers and Abilities
Little has been explained about the nature of Pulse's power. However, he seems to be able to nullify & neutralize the powers of other mutants. This enabled him to physically contact Rogue's skin at a time before he had gained full control of her own powers. He appears to have more control over his abilities than the MorlockLeech, and seems to be able to specifically select his target unlike the Fallen AngelChance.
During the fight against Death (Gambit), Pulse proclaimed that he had used Death's own ability to create poisonous gasses inside Death's body. Therefore it appears that Pulse has the ability to activate other mutants' powers and redirect them remotely.
A physical & visual sign that Pulse is using his powers is in his eyes. The glow a golden color pulses from his eyes.
A skill that doesn't rely on his mutant powers, is the ability to break & enter into properties without being detected. Pulse is silent on his feet, deft at picking locks, and swift when making his get-away.