(the fixnum (compute-my-fixnum-value))
This specifies that the value in the form in the second argument is of the type specified by the first argument. One might assume that this is what other languages call `assert`, and it can be; your compiler / interpreter can be configured to assert if it detects a mismatch between the two.
... but the spec actually specifies that if they don't match, the behavior is undefined. `the` is also an opportunity for the compiler to throw away some dynamic typechecking logic; essentially, it's a chance to paint racing stripes on the implementation so it goes faster at the cost of risking undefined behavior.