(covers information from several alternate timelines)
A pattern enhancer, also known as a transporter/transport enhancer, was a piece of portable equipment that boosted the signal of the transporter in conditions where a signal was otherwise difficult to maintain.
By the late 24th century, pattern enhancers were about one meter in height, composed of four sections: a trio of legs which were encased within the body while not in use, highly-polished silver-colored main body casing, a black control cuff, and roughly conical top which glowed when activated and in-use.
Used in sets of three, the enhancers were set up in a triangular formation, approximately one-to-seven meters apart. First the legs were extended by means of a switch on the main body, enabling steady placement regardless of terrain. Second, the conical top and the attached control cuff of the device were rotated approximately 70-90° clockwise; once the top was lit, the enhancer was active. (TNG: "Power Play")
In 2257, a cloud of charged particles disrupted the transporter signal to investigate the crashed USS Hiawatha. The away team resorted to landing pods to get to the ship, and brought transporter enhancers to get back. (DIS: "Brother")
In 2263 of the alternate reality, Montgomery Scott came up with the idea of modifying pulse beacons from the USS Franklin to act as pattern enhancers to enable an away team to beam the trapped crew of the USS Enterprise out of Krall's base. These makeshift pattern enhancers successfully enabled Scott and Pavel Chekov to beam the Enterprise crewmembers, twenty at a time, to the Franklin. (Star Trek Beyond)
Responding to a distress call in 2368, an USS Enterprise-D shuttle crashed on Mab-Bu VI. EM bursts prevented a stable transporter lock on the away team, but Transporter chief Miles O'Brien volunteered to beam down with a set of pattern enhancers. Set seven meters apart, the enhancers allowed Enterprise to retrieve the team. (TNG: "Power Play")
In 2369, while Professor James Moriarty trapped Captain Jean-Luc Picard, Lt. Commander Data and Lieutenant Reginald Barclay on the Enterprise holodeck, in a scheme to escape the confines of the holodeck, Barclay set up transporter enhancers within the Sherlock Holmes simulation in an effort to "enhance the molecular pattern of [a] chair... so the transporter can get a better lock on the signal." (TNG: "Ship in a Bottle")
Investigating unusual activity on Devidia II, pattern enhancers were used in conjunction with phase conditioners and phase discriminators to adjust the phase of Captain Picard, Riker, Troi, La Forge, and Crusher so they could see the Devidians. (TNG: "Time's Arrow")
In 2370, Lt. Commander Data set up pattern enhancers on Atrea IV to allow himself and Juliana Tainer to beam back to the Enterprise, though the enhancers were destroyed in a cave-in. (TNG: "Inheritance")
In 2371, while attempting to rescue an apparently trapped Major Kira Nerys, Odo asked the computer if using pattern enhancers would allow the runabout to lock onto her signal, but the moon's polarized ionization field made it impossible. (DS9: "Heart of Stone")
After detecting an omega molecule, Captain Kathryn Janeway and the crew of the USS Voyager were left with little option but to construct a harmonic resonance chamber to destroy the molecules. Pattern enhancers had been set up in the alien laboratory to ensure the transporter had a stable lock. (VOY: "The Omega Directive")
While hiding the telepathic Brenari and Voyager crew members that were telepathic from the Devore, the crew devised a method of using pattern enhancers to conceal the telepaths in transporter suspension without leaving a record the Devore inspection teams could find. (VOY: "Counterpoint")
While attempting to recover the Friendship One probe, Chakotay led an away team to an alien planet with an irradiated atmosphere. At a distance of less than 3 kilometers, radiation levels of 6,000 isorems required the team to bring pattern enhancers to transport the probe. Before the team could set up, they were taken prisoner by Otrin and his people, who allowed Lieutenant Joe Carey to set up the enhancers before killing him as he was being beamed to Voyager. (VOY: "Friendship One")
The shorter enhancer was not accompanied by the common blue-triangle effect in "The Alternate." A different miniature enhancer design was introduced in "Friendship One" which more closely resembled the larger model and did use the blue-triangle effect.