why do we safely remove hardware

When you plug in a USB drive, you give your PC free reign to write and read data from it; some of which is cached.

Caching occurs by not writing information immediately to the USB device, and instead keeping it in your PC's memory (RAM). If you were to yank the USB drive out of your PC before this infromation is written, or while its being written, you'll end up with a corrupted file.

However, Windows automatically disables caching on USB devices, unless you specifically say that you want it enabled. For the most part you don't have to click the 'Safely Remove Hardware' button, if you aren't writting or reading anything from the device.

Its there simply as an extra level of security preventing you from destroying your own files.

Doing so causes the files to close "gracefully", preserving data, pointers and file size indicators. When writing to disk the computer doesn't always "flush" a buffer and only part of the data may have been written. Using the proper procedure will assure that the data and pointers are in good shape.

References:
http://wiki.answers.com/Q/Why_click_safely_remove_hardware_icon_on_USB_flash_drive