The self-replicating mine is a defensive explosive device invented by Miles O'Brien, Rom, and Jadzia Dax in 2373. The mines were deployed in a field around the entrance of the Bajoran wormhole, to prevent any further Dominion reinforcements from coming through. Each mine was cloaked and extremely small, no more than a meter across, which prevented advanced Dominion sensors from detecting them. More importantly, the mines were equipped with a replicator unit, such as that every mine that was detonated or deactivated would be immediately replaced by its neighbor. The mines were programmed to swarm-detonate, to compensate for their small size. (DS9: "Call to Arms")
Due to the possibility of the mines' proximity sensors causing premature detonation, the entire minefield had to be put in place before the mines could be activated. The Dominion sent a fleet to prevent this from happening, but cover fire from Deep Space 9 and the IKS Rotarran allowed the USS Defiant to complete the task. The activated minefield proved an effective barrier to the Dominion even after Deep Space 9 was captured. This frustrating obstacle prevented the Dominion from overrunning the Alpha Quadrant. (DS9: "A Time to Stand")
Eventually, Damar found a way to deactivate the mines without having them replicating themselves, by isolating them one at a time with an antigraviton beam projected from Deep Space 9's deflector array. Fortunately, through Morn, Kira Nerys gave Starfleet information on the deactivation of the minefield. Faced with the prospect of overwhelming Dominion reinforcements through the wormhole, Starfleet launched Operation Return, sending all its available ships to destroy the deflector before the deactivation process was completed. Unfortunately, the Defiant arrived too late to prevent Gul Dukat from detonating the minefield, forcing Sisko to send the Defiant into the wormhole to confront the Dominion reinforcements. (DS9: "Behind the Lines", "Favor the Bold", "Sacrifice of Angels")
According to Star Trek Encyclopedia (p. 290), the mines were labeled "ALH 84001" as a reference to the meteorite Allan Hills 84001, which was found in 1996 to have fossils of micro-bacteria from Mars.
In the Star Trek: Deep Space Nine Technical Manual more detailed information is given of the self-replicating mines. Their shells are described as duranium cargo containers. They are cloaked with miniature cloaking devices and have proximity and contact sensors for detonation with a neutrino source counter for distance keeping with one another, a thruster system of a class-1 probe with a single fuel source designed for station keeping and a combiner tank with a premixed charge of a standard photon torpedo warhead serves as the explosive.
The replication system is further explained as well. Each mine has initially only 1/65 of the material stored in them for a single replacement mine. Replicators however transfer material to one another where it is needed in the field through networking. As stated in DS9: "A Time to Stand", the neighbor of a detonated mine does seem to replace the lost mine in the end, material however comes from at least 65 different mines. As stored material begins to run out the mines have a zero-point extraction system for matter replenishment.
Based on the figures given in the manual, the field laid out by the Defiant contained some 165,000 mines altogether. Judging from the visual effects in the episodes this isn't so far fetched. It is unclear if the use of cloaking devices in mines violated the Treaty of Algeron. There has never been any specific reference to this type of use being banned. The Federation has also been observed using isolation suits and a cloaked holoship in Star Trek: Insurrection.
In the novel The War of the Prophets, Garak reflects that, when he first heard about Rom's role in designing the minefield, he was so impressed that he actually used some of his intelligence contacts to determine if Rom was actually living under an assumed name to escape the burdens of a genius past, but is forced to concede that Rom appears to be exactly what he claims to be after his search efforts reveal nothing untoward.
In Greg Cox's Tales of the Dominion War short story "Night of the Vulture", a Cardassian double agent on Earth obtains the codes from Starfleet to deactivate the minefield. En route to Terok Nor, however, the ship transporting the spy and a Founder is attacked by the Beta XII-A entity. Everyone aboard is killed, although the ship and the entity are pulled into a spatial rift.