The idea is that if someone was silently in your account, and doing a "stealth" attack - then they could change your password, then change it back to your original password, thus "resetting" your expiring password timer, giving them more time in the system - and you would not know that the password was reset. Preventing old passwords prevents this.
Note: The only flaw I never understand with the above is cant the attacker just change the password like 10-15 times in 5mins, and thus "flush" out the old password?
Note 2: I dont personally agree with expiring passwords - but it helps understand the reason why it exists.