A tachyon burst is a concentrated pulse of tachyon particles which has a number of uses.
The Tigans used tachyon bursts in their interface system. Minute bursts were used to transmit new data from their central computer to interface implants which delivered information directly to each individual Tigan's cerebral cortex. (TNG - The Space Between comic: "History Lesson")
Firing tachyon bursts at a shielded starship can disrupt the shields, forcing the ship to remodulate and offering a brief window of opportunity in which a transporter beam can reach targets within the shielded ship. Lieutenant Commander Worf and Captain Picard attempted to use this technique to capture a malfunctioning Data from a Venture-class scout in the year 2375. Not long after Data himself used the same technique to force a Son'a starship to remodulate its shields so that the crew could be transported away to a location where they could do no harm. (TNG movie: Star Trek: Insurrection)
In 2376, Nog and Thirishar ch'Thane discovered that tachyon bursts could be used to disrupt Iconian gateways, based on evidence from Alexandra's Planet. The USS Defiant later used a tachyon burst to close a gateway near Europa Nova. (DS9 - Gateways novel: Demons of Air and Darkness)