The Preacher

 refers to an unmarked quest in Fallout 3.

There is a Wastelander (commonly known as "The Preacher") standing on the second floor of a building in an alleyway west of the Reilly's Rangers headquarters entrance on Seward Square. The alley has been rigged with Mines and Mini Nukes that he detonates if you try to get close to him. There is a hostage (another Wastelander) on one end of the alley, who you can talk to. If you are looking at the Preacher when he detonates, he waves at you. He also dies in the blast.

Resolving the situation
If your stealth is high enough, you can sneak through and pick up the Frag Mines (at least five) and multiple Mini Nukes (there are at least five; one behind and one in between the barrels by the slide, one next to the shopping cart, one on some rocks across from the shopping cart, and one on the merry-go-round.) Even without the Light Step perk, the explosives will not detonate if you step on them as they are intended to explode only when triggered by the preacher. Alternatively, you can use Dogmeat to find ammo, pick up the mininukes, or find weapons and pick up the Frag Mines. However, removing all the nukes and mines off the ground will still NOT stop him! The Preacher can still cause a deadly explosion if he sees you in the alley. There are at least five more Mini Nuke detonations that can't be stopped.

The only sure way to stop the Preacher and the detonations is by killing him. This can be achieved by getting to a position where you can properly see him and picking him off with a well-placed shot with scoped weapon like a Sniper Rifle, or Scoped .44 Magnum. A good spot from which to shoot is next to the Wastelander (hostage who asks you for help). Be careful though, because if the preacher sees you, he will order you to freeze in your position, and any movements can cause him to trigger the explosives. More importantly though, if you take the shot but somehow miss, he will detonate the bombs. Firing at him with weapons like the Missile Launcher (which take longer to hit him) may cause him to detonate before he dies as well. Tossing a Frag Grenade into his hiding spot while out of sight is also an option for killing him.

You can also talk the hostage into confronting the Preacher using Charisma (a score of 1 is required), which will cause him to boldly run towards the preacher to talk to him. At this point it would be wise to back away from the alley. You get no Karma change for this and you get to view a spectacular fireworks show.

An alternate method (confirmed on PC) is to throw a frag or plasma grenade into the alley and backpedal. The preacher will be killed by the resulting explosion. This route nets no reward, or karma change.

Reward

 * 5 Mini Nukes
 * 5 Frag Mines

Frag Mine Locations

 * 3 clustered in the center
 * 1 underneath children's slide
 * 1 on broken piece of teeter-totter

Mini Nuke Locations

 * 1 behind three metal barrels
 * 1 in between those barrels
 * 1 on a pile of rocks to the immediate right of the boarded up Preacher's door
 * 1 on far side, on a merry-go-round
 * 1 immediately next to or in the shopping cart (opposite the door)

Quotes
General
 * "And the sun will rise in the north! No! the northwest! For forty-four days and sixty-seven nights! And we'll never notice!"
 * "You don't know, you can't know. Little fools. You wish you knew! You wish! But only I know! Only me... only me... only me..."
 * "The sky will fall! The Earth will rise! The stars will shine open their toothy grins and caress the sun with their love!"
 * "THE SUN! IT BURNS! Why does it burn? Why have we put the sun into a jar? And what did we do with that jar? We broke it all over our little world..."
 * "Fire, fire, burning bright... burning... fire... pain, misery, peace, love, murder, death, death, death... love..."
 * "Trees! So many trees! To the north! But be careful... the trees... are deadly, and the trees too will be consumed in the belly of the great fat worm!"
 * "A great crack shall open in the Earth and swallow the non-believers! And they shall weep! Weep! Weep! Tears and salt and earth and dirt!"
 * "Try new BLAMMO! Soap! Blasts stains out! Blasts the whole world out! We've all been BLAMMO'd!"

After Detecting the player is near
 * "Not one step further! Not one! Come no closer! I'll do it! I'll blow us ALL to hell! All of us! Me, you... and the worm..."
 * "Beware, worm! I shall destroy you! With the fire of this small sun before me! BEWARE WORM! Not one step further!"
 * "Hungry... hungry... so hungry. What? No. I'm not hungry. The worm is hungry. Hungry for me, for you, and for fire"
 * "In fourteen hundred and ninety-two, your mother and my mother were hanging up clothes around the mulberry bush..."

Trivia

 * The "great fat worm" is possibly a reference to the poem The Conqueror Worm by Edgar Allen Poe, or Shai-Hulud, a giant worm featured in the Dune book series by Frank Herbert.
 * He also talks about putting the sun in a glass jar, and "breaking it over our little world," which could refer to the nuclear weapons used in the Great War, especially since he threatens to kill the player with the "small sun before [him]."