WTF? I hear you think. Quite - this is as arsy a bit of legal gobbledegook as you're likely to come across. It means you and the publisher can write to each other using the postal service and the normal assumption will be that the letters will arrive at their destination fairly promptly. So - you may use the last address you have for the publisher, and they may use the last address they have for you. It's easy to check a publisher's address as it will be online. It's less easy for the publisher to check your address because you aren't stupid enough to have your address online, are you? This means it's important to keep your publisher informed of any and all changes of address. All your publishers, that is. If the publisher(s) deal with your agent, this isn't quite as important, but it is still good practice to do so. What if your agent retires or dies, or you part company? Yes, they should inform your publisher (not of their own death, obviously) but you don't really want to rely on them to do so.
in due course of post = next day or so for first class letters, a bit longer for second class letters at the moment. But this can change in certain circumstances - such as during a postal strike, or at some point in the future when the postal service is routinely worse than it is now. The clause means the normal state of the post prevailing at the time you send the letter.
Of course, we don't really send letters to our publishers using the postal service. Apart from sending back contracts, I don't think I've sent an envelope to a publisher for years. It is important to keep your publisher informed of your email address, as that is the usual method of communication. The best solution is never to change your email address - I feel a post about email addresses coming on. If you use the email address given to you by your ISP, you'll lose it when you change ISP. It's much better to register your own domain. Yes, we'll do a post on email addresses and domain names. (Some people use the phone - if you do that, make sure your publisher knows your phone number. I spend half my time trying to get publishers to forget my phone number as I hate phone calls.)
That's it for notices. There are two clauses left, and they are not very interesting. Not selling this, am I? At least they're short.