By default, when you tap a key using the iPhone's built-in virtual keyboard the device makes a "tapping" noise. This is to mimic the sounds that you would here if you were using a real keyboard with the device. If these sounds aren't to your liking, you can enter the iPhone's "Settings" application and change both their volume as well as whether or not you hear them at all.
Turn on your iPhone.
Use your finger to slide the volume indicator bar and set your ideal volume for the keyboard sounds on your iPhone. Sliding the bar to the left turns the sounds down, while sliding the bar to the right turns them up.
Tap the "Keyboard Clicks" category listing to turn the keyboard sounds from "On" to "Off." When off, the virtual keyboard will make no noise when you use it.