Squeezing is an advanced technique used by many Guitar Hero players to get a higher score than normally possible. Squeezing is much easier in GHIII due to the very large timing window.
1: Activate star power on or slightly after the first note in the activation
2: Immediately strum the note (this takes advantage of the timing window; in effect you have activated star power after the note, but the note still counts as under star power)
3: On the last note under star power, strum as early as possible (without it counting as an over-strum) so that the note is also included in the phrase.
In effect, a squeeze adds a note to the activation. If you squeeze a single note, you would gain 400 points, 800 for a 2-note chord, and 1200 for a 3-note chord.
Notice the blue flames at the beginning and end of the squeeze. These prove that the squeeze was successful.