Observers are genetically enhanced humans from the future. They were designed to be faster, stronger and smarter. They are able to perceive time differently then regular humans.

Do we know how they obtained that power though

Yeah I looked at that already thanks

I was looking for in detail analysis other than just future technology

I think we're supposed to believe that it's a side-effect of being able to essentially see the future. That doesn't really address the physics of the impact of a bullet, but I think we're supposed to believe they know where the bullet is going to be fired and so they know where they can intercept it and their super-speed allows them to do that.

Is that more what you were trying to get at?

Yeah thats fine thanks

What I can tell you about these characters is that they are based on the description of The Watchers from The Complete Book of Enoch. Read it for some insight on what they are exactly.

Thanks

Sorry if I'm late to the party, but I just thought I'd weigh in.

IMO, it's a side effect of their ability to move through time. They had several time based abilities: precognition, time travel, parallel timeline travel, and their ability to manipulate their personal time frame. What do I mean by that last one? They're essentially much weaker versions of a guy named Zoom in DC comics. He wore a similar costume as the Reverse Flash, but was a different person with different powers that resembled superspeed:

They've probably changed things now, but originally Hunter Zolomon gained the ability to control his own personal timeline. His place in time was detached from everyone else's. He sped up his timeline to move at superspeed or slowed down his own timeline to move slower. This made him faster than the Flash.

In Fringe they don't really go into detail how they catch bullets, but there are clues. In S4 E22 Brave New World: Part 2 where Olivia kills the woman that shot September the woman calls their ability to catch bullets "hyper-attenuated time."

JESSICA HOLT: (smug) "I hate kids. Now let's see how concerned you are about him." (fires pistol three times at The Observer. all three projectiles are easily caught, then discarded. to Olivia) "They can operate at hyper-attenuated time. To us, it almost looks like magic. It's not, though. It's just tech that essentially lets them move very, very fast." (unholsters new pistol and aims it) "Now this gun is an invention of Doctor Bell's. Shoots faster." (fires weapon and strikes The Observer, with the round passing through his palm and left shoulder. blood erupts from the injury)

In the 4th season episode 15 Walter discovers that something happened when September disappeared off the operating table where they were trying to save him. He uses a device that slows down events occurring on video until you can see events that occur so fast you supposedly can see individual particles of light. They witness September being kidnapped by Observers. They also witness September moving so fast the other Observers fail to notice him putting something in Peter's eye even as they're kidnapping September.

I submit he's not using actual speed to do this. He's messing with his personal timeline. He's like a master of Relativity and the opposite of the Twins in Einstein's Twin Paradox. Time in his own personal frame of reference is accelerated, while it marches at a different rate for everyone else's frame, who either doesn't have or is less adept at using this ability. To any outside observer in a slower reference frame, he would look as if he were moving rapidly, even though he's just moving at normal speed in his own reference frame. His reference frame is accelerated relative to all outside observers in slower frames.

Ok thanks for explanation.