High-energy phosphate can mean one of two things: High-energy phosphate bonds are usually pyrophosphate bonds, acid anhydride linkages formed by taking phosphoric acid derivatives and dehydrating them.
As a consequence, the hydrolysis of these bonds is exergonic under physiological conditions, releasing Gibbs free energy.
The squiggle notation was invented by Fritz Albert Lipmann, who first proposed ATP as the main energy transfer molecule of the cell, in 1941.
Lipmann’s term "high-energy bond" and his symbol ~P (squiggle P) for a compound having a high phosphate group transfer potential are vivid, concise, and useful notations.
This effect is due to a number of factors including increased resonance stabilization and solvation of the products relative to the reactants, and destabilization of the reactants due to electrostatic repulsion between neighboring phosphorus atoms.