The expanding energy pulse was a type of phaser discharge 24th century Starfleet phaser rifles could be reconfigured to fire. After firing, the pulse expanded to a bolt of phaser energy, roughly a meter across.
In 2371, the crew of the USS Defiant used expanding energy pulses to carry out a phaser sweep of the entire ship, every corridor and conduit. They were looking for the changeling Founder who had replaced Ambassador Krajensky. The expanding pulses were used as they could be set low enough to avoid damaging equipment but high enough to affect the changeling. The modified phaser beam had the side effect of heating up the air the pulses traveled through. (DS9: "The Adversary")