(covers information from several alternate timelines)
In the year 2263, Krall used his swarm to attack the Federation starship USS Enterprise under the command of Captain James T. Kirk. Approaching the Enterprise in orbit of Altamid, these ships initially appeared to be one large vessel, emitting an unidentifiable signal, but quickly separated and attacked in a coordinated effort to disable the Constitution-class ship. Surrounding and ramming it repeatedly, these ships inflicted serious damage on the Enterprise, first severing its warp nacelles before finally separating its primary hull from its secondary hull.
Krall later used his ships to attack the Federation Starbase Yorktown in a massive assault. Utilizing antique equipment aboard the century-old USS Franklin, the Enterprise crew was able to identify the swarm ships' signals as closed networked cyberpathic communications that allowed them to coordinate their maneuvers. Emitting VHF radio signals in the form of "classical" music by the Beastie Boys, the Franklin flew very near to Krall's ships, causing a chain reaction that destroyed the swarm.
Once again flying a commandeered swarm ship, Spock and McCoy assisted James Kirk in defeating Krall within the Starbase Yorktown before Krall could unleash a super weapon and kill the base's inhabitants. (Star Trek Beyond)
Swarm ships were capable of space and atmospheric flight, and were equipped with warp drive. They were piloted by two drones and, when not in use, docked in tree-like formations at towers on the surface of Altamid. The ship is accessible through a circular hatch in the rear.
Though apparently lacking weaponry, Swarm ships were durable enough to inflict heavy damage on other ships by ramming them. When colliding with another ship, a Swarm ship could elect to penetrate only partway and deploy its lateral prongs to anchor itself; the nose of the ship could then split open to release drones inside the target vessel. Swarm ships were susceptible to phasers, but operate in such large numbers that phaser fire was overall ineffective against them. They were too small and nimble to be effectively targeted by photon torpedoes. (Star Trek Beyond)
The ships were named "Krall swarm ships" in a Popular Mechanics cutaway diagram of the Enterprise.
The idea of relatively very small ships that swarm to engage their enemies was thought up by Justin Lin and considered over a long time by him. When he suggested that concept as the director of Star Trek Beyond, the other filmmakers who were working on the movie liked his idea. "The swarm was always in play," stated Star Trek Beyond Co-Writer Doug Jung. "I think that was again something that Justin always wanted to do [....] He's like, 'Why would you have that big ship going around? Why not just get a bunch of little ones?' And I was like, 'Yeah. Guess it makes sense!'" The idea of using small vessels also helped the team achieve a goal they were aiming for, as they wanted to make the space battle sequences in the movie less like the submarine warfare genre of films than was usual for such scenes in Star Trek. 
In the first trailer for Star Trek Beyond (which was released on 14 December 2015), Krall's swarm ships appear maroon in color. However, in the film's second trailer (which was released on 20 May 2016), they appear dark gray or black in color, as they do in the finished film.