Check them. It'll vastly improve compiled code performance, because it reduces extra code which validates for errors, and is included by the compiler.

Removing them, however, makes this code work:

Code:
Dim ABC(0) As Long
ABC(1) = 1
It will error in IDE, but works compiled when "Remove array boundary check" is checked, because additional code by compiler is not included which would check if index 1 is a valid index for that array.

For this kind of reasons these "advanced optimizations" are dangerous and you must know what they do, and avoid writing code that depends on such errors.