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The technique of squeezing intuitively emerges from the Guitar Hero series' concepts of Star Power (or Overdrive, as it's known in Rock Band), and the timing window; leeway given on the preciseness of your timing. Since Star Power doubles the score you receive from each note, careful planning of the activation points must be considered to optimize one's score, as you generally want to get the most notes possible before your Star Power meter depletes.
The basic idea of squeezing is to delay strumming the first note under your activation; play it as late as you can without missing it, then quickly activate Star Power microseconds before the strum. By doing this, you are able to "squeeze" in another note, just as your Star Power depletes, by strumming it early.
It's generally considered easier to perfect this skill with the use of the select button to activate Star Power, rather than the less-precise tilt sensor.
In some cases it is possible to perform double squeezes, or even triple squeezes, based on the song's notechart, rhythmic properties, and your ability to exploit the timing window as much as possible.