The offer start date and the offer end date determine when coupons can be issued (the dates are inclusive).
The redemption start date and the redemption end date determine when the coupons can be redeemed (i.e.used).
For example, you might want your customers to be able to get their coupon during the month of February. But they can't use / redeem the coupon until March.
This can be a powerful technique to use if you want to wait to find out how many people sign up for the coupon, before allowing anyone to use the coupon.
Important to note that dates can overlap. For example the most common usage is when offer start date = redemption start date and offer end date = redemption end date.
But note that redemption start date can never be before the offer start date. i.e. you can't use the coupon before you'e got a coupon! ;-)