How is sign extension used in practice?
You sign-extend anytime you need to increase the number of bits in a value.  Usually, this is done right before you do mathematical operations on two values.  For example, when you add two signed integers, the number of bits in both numbers needs to be identical.

There are many reasons why you might not have the same number of bits in two values.  One value might be a 16 bit integer, while another might be a 32 or even 64 bit int.  The number doesn't have to be a a multiple of 8 bits either-- there are many analog-to-digital converters that do 10, 12, or 20 bits.