There is no need to go overboard with fitness preparation for climbing Mount Kilimanjaro.
However, climbing Mount Kilimanjaro is a physical undertaking, so you should prepare yourself accordingly with a Kilimanjaro training program.
Being in good shape is important in many aspects - obviously strong and conditional legs make it easier to walk uphill and downhill for sustained periods of time.
Finally, a positive mental attitude can work wonders for you when fatigue and doubts arise.