It keeps your code tighter. It mostly helps me keep more aware of what is going on in my code. With option strict on, you cant make a narrowing conversion or cast without knowing it. With option strict off, people sometimes find themselves doing things like adding the numeric values of strings instead of concatenating them, or treating one type of object like another.
Sometimes it is a little extra typing because you have to explicitly code all narrowing conversions (Integer to byte, String to integer, Object to Control, etc.) but it also helps because you cant perform a cast or conversion that could potentially cause errors without knowing it.