When you talk, sound is produced by passing air over our vocal cords (flaps of tissue in our throats) causing them to vibrate. The vibrating vocal cords make the air around them vibrate and this makes sound.
Now for the physics bit. You know how sound is in the form of waves? The wavelength can be related to the speed with which the wave is moving and the frequency (how often a single wavelength passes a fixed point) by this formula:
Wavelength = speed / frequency
The speed of a sound wave depends on what it is trying to move through. For example, sound moves faster through water than through air, which is why you can hear a boat heading towards you from a much greater distance if you stick your head under the water. Or when cowboys stick their ear against the ground to hear what trouble is coming their way (not sure if they actually do this in real life or just in the films!). Normally, we breathe air, which is a mixture of gases containing mainly nitrogen and some oxygen. Sound waves generated by our vocal cords move at a constant speed of around 350 meters per second.
While the speed of sound waves remains constant, the wavelength of the vocal sound waves depends on the shape of our throats and mouths. We can therefore alter the pitch of our voices by moving our throats and mouths (try speaking without moving your mouth - you’ll find it’s much harder than usual). Because the speed of the sound waves is constant, if you increase the wavelength you reduce the frequency and our voice gets lower. It's pretty simple: High frequency = high voice, low frequency = low voice.
Now the fun bit is when we start thinking about what happens if we breath in helium. Helium is less dense than the air we normally breath and this means that sound waves travel through it much faster than usual (around 900 meters per second). The wavelength of the sound waves is unaltered by the helium as this is determined by the shape of our throats and mouths. This means that if you increase the speed of the sound waves, the frequency also has to go up and this means that our voices sound much higher than usual.
So if a lighter gas like helium gives us a higher voice, wouldn't a denser gas like Argon or Xenon make our voice deeper? This is true, but the problem is that these gases are harder to get hold of than helium. Xenon for example is very expensive, and in addition, it has anesthetic properties similar to nitrous oxide, so you can get a little high if you breath it. Just take my word for it and don't try it for yourself.
Something to remember: Although helium is un-reactive, it can still kill you. If the entire room was filled up with helium, you would quickly asphyxiate due to there being no oxygen present. Please do remember this if you insist on breathing in helium - while a balloon-full isn't going to do you any serious harm, that lightheaded feeling you get after breathing in too much balloon gas is a sign that you're not getting enough oxygen into the lungs and you should probably give the balloon breathing a rest.
