The word itself is a portmanteaux of Squirt and Midget, implying shortness of stature, but the scope is far greater. A squidget is a genuinely detestible person, usually obnoxious and overweight, with an intense, selfish greed. Generally annoying and one of the worst examples of humanity you can find. Often heard screaming "REEEEEEEEEEEEEEEEEEEEEEEEEEEE" when they don't get their way.
"No, I won't give you what you want, you stupid little squidget!"
"Man, you know that kid? What a fucking squidget."
Usually far more drawn out than written above, along the lines of "REEEEEEEEEEEEEEEEEEEEEE". It's the sound heard when someone decides to whine about a particular situation, be it something they want, or something happening to them. Typically a sound associated with squidgets.
Also, this word can be thrown in the face of said whiner to tell them precisely what you think of them.