(covers information from several alternate timelines)
A Tholian web, also known as a tractor field, was an energy net that was "spun" by Tholian 22nd and 23rd century spacecraft around an immobilized enemy vessel. The more vessels that were used to generate the web, the faster it was deployed. A web can be disrupted by destroying the ships creating the web before they finish. (ENT: "In a Mirror, Darkly", "In a Mirror, Darkly, Part II"; TOS: "The Tholian Web")
The web was composed of a series of energy filaments which were generated in a web pattern around a target vessel. Once these filaments were sealed, the web became self-generating and the web-spinning crafts no longer needed to maintain the web. If any craft within the web attempted to leave, they would be shredded by the energy filaments. Outgoing weapons fire, such as photonic torpedoes, were also destroyed by the web and the resulting detonation energy was dispersed across the energy filaments. However, ships outside the web could fire into it without hindrance. (ENT: "In a Mirror, Darkly")
The filaments were generated by specialized craft that emitted them from the aft section. At least two ships were needed to spin the web - if one broke away prior to web completion, the filaments would presumably dissipate. (TOS: "The Tholian Web") Webs can be generated in less time if more ships are available to complete them. (ENT: "In a Mirror, Darkly")
In 2155, the ISS Enterprise NX-01 was destroyed while caught in a Tholian web. Several escape pods from the Enterprise were also destroyed as they attempted to traverse the web, although some were able to leave through the gaps. (ENT: "In a Mirror, Darkly")
The Tholians proceeded to form another web over their docking portal to prevent surviving Enterprise personnel from escaping aboard the USS Defiant; however the Defiant destroyed the Tholian ships and escaped. (ENT: "In a Mirror, Darkly, Part II")
In 2268, the USS Enterprise was nearly trapped inside of such a web while on a mission to rescue Captain Kirk from spatial interphase. The Federation starship narrowly escaped being dragged back to a Tholian port as they were able to leave the web before it was complete. (TOS: "The Tholian Web")
The effects for the Tholian web in The Original Series, as originally aired, were created by Mike Minor. He commented on his work:
"The design of the web was based on the geometry of a geodesic dome. I ignored the fact that when you interlock ready-made triangles within a dome, you don't have horizontal and parallel lines – you have zig-zag connections. As time was short, I went for a very simple design in which the ship simply made a horizontal movement left to right or vice versa. Any given shot could be flopped in the printer to its mirror image. I also set it up to do 45° diagonal movements from the bottom to the top of the frame. These pieces could be flopped or combined to make up any specific shot. Once they shot the model of the Tholian ship against black velvet, I projected the shots a frame at a time onto a white card, with a rotoscope set-up, and plotted pencil marks where the ship moved by tracing and advancing each frame. Then I created the cel-like cartoon animation using black lines for the grid. Each shot in the episode showed a partially completed grid with one line being animated across the field as if by the Tholian ship. I shot those by pulling a white card frame by frame revealing the black line underneath. A black-and-white negative of all this resulted in a black background with white or clear lines on the film which was used to create an animation burn-in." (Starlog, issue 25, pp. 36 & 61)
The Tholian web is a staple part of the tactical combat wargames of the Star Fleet Universe, such as Federation Commander (where full rules for web will be formally published in the upcoming Tholian Attack module) and Star Fleet Battles.
In the SFU, there are two prominent types of devices that can produce webs - the Web Generators (attached to 'Archaeo' Tholian ships - such as the Patrol Corvette, the SFU reference for the ships seen in the Original Series) which allow a ship to 'spin' web, and the more powerful Web Caster (usually seen on larger 'Neo' Tholian ships - designs unique to the SFU) which can project web at long range, or produce a concentrated web 'fist' capable of acting as a direct-fire weapon.
In the SFU setting, the Tholians arose in M81, where they eventually established a galaxy-wide empire - in which the use of web was key to their ability to suppress opposition. Indeed, the Seltorian race (a species of insectoids granted 'most-trusted-race' status within the Tholian Will) only managed to overthrow their masters once they discovered the Web Breaker - a weapon uniquely capable of disrupting the web. When the Tholian remnants who fled to the Milky Way established their Holdfast, web was once again the key to their survival in the face of hostile neighbors (such as the Klingons).