The usual definition is a fractal one: a bar is a swing high if the bars immediately before and after it have lower highs. Larger lookbacks, for example two or three bars each side, produce fewer and more significant swings.
Swing highs are the raw material of market-structure. Sequences of them define whether price is making higher-highs-higher-lows or the opposite, they anchor fibonacci-retracement draws, and they mark the levels where resting stop orders from short sellers accumulate.
The catch is that a swing high can only be confirmed after the bars to its right have printed, so the label always arrives late. Indicators such as zigzag-indicator that mark swings are subject to the same delay and will repaint their most recent point.
Related: swing-low, market-structure, zigzag-indicator, equal-highs