It sounds like whistling to some and screaming to others, but the high-pitched sound coming from your toilet tank while it's refilling just means your toilet -- or at least the fill valve -- isn't working as well as it used to. If you don't mind the sound, you can let it be for now, but it isn't difficult to fix.
Obsolete Toilet Technology
If you look into your toilet tank, you'll probably see a metal ballcock-style fill valve, and the chances are the tank itself is an example of the 5 1/2-gallon tanks that were common before 1992, the year that low-flow technology became mandatory in the U.S. Although contemporary toilet manufacturers continue to supply ballcock-style valves with their toilets, they make most newer ones out of plastic. The older metal ones tend to corrode and stay partially closed when the tank is filling, especially when the tank is almost full. Pressurized water rushing through the partially open valve and making the metal vibrate is what creates the high-pitched sound.
A Quick Fix
If the sound bothers you and you don't have time to replace the valve -- or the toilet itself, if you have an old water waster -- you may be able to lubricate the valve so that it will open wider. To do this, turn off the water, flush the toilet and let the fill valve dry out. Spray lubricant at the point where the float arm meets the valve body while you move the float up and down. The lubricant should improve the valve operation temporarily, but the sound will probably return after the valve has been underwater for a few weeks.
Replacing the Fill Valve
The way to permanently eliminate the high-pitched squealing is to replace the fill valve, which isn't as difficult as it sounds. It isn't expensive, either, because new valves cost less than $20. You remove the old valve by unscrewing it from the bottom of the empty tank; the locknut may be corroded and require generous amounts of lubricant. After determining that your new valve fits the tank and flush valve, you screw it into the hole from which you removed the old valve and reconnect the water. Fine-tuning the float to get the proper water level in the tank completes the procedure.
Replacing the Toilet
If your screaming ballcock is part of a water-wasting toilet, it's time to replace the toilet. You may be surprised by the amount of water you'll save. If you're an average person, you flush five times per day, and each flush of your new toilet will save up to four gallons. This means that a family of four could fill an average-size swimming pool with the water they save every year. Replacing an older toilet with a low-flow model is usually a straightforward job that takes about an hour, and you won't have a recurrence of the screaming because new models doesn't have any metal parts.