This is a short and easy clause. You just have to make sure it's there, really.
7. Author's Name and Copyright Notice
The Publishers undertake that the name of the Author shall appear on the title-page and on the cover or binding and jacket of every copy produced and that the following copyright notice shall be printed in every copy of the Work:
Copyright in the text Stroppy Author 20**
**indicates the first year of publication
You should make sure the publishers include this: it's vitally important to keep your copyright if you possibly can. It should always be possible with fiction, though if you are writing for a series sold into schools you might have to argue.
In the case of children's non-fiction, particularly that commissioned as part of a series intended for sale into schools and libraries, you may not have this clause. This type of work is often considered 'work for hire'. You can, if you wish, try arguing that you want to keep copyright and license the text to them, but I don't give much for your chances. Full sale of copyright is standard in many areas of children's non-fiction. I don't argue about this one, nor do most children's n-f writers. If you don't have the copyright clause, the work will usually pay a flat fee and no royalty. The publishers can re-use the work, re-issue it without telling you (though that is not polite) and produce it in different formats without paying you more or telling you. As long as you retain moral rights (we'll come to that) they can't just ransack it and use gobbets, or rewrite chunks of it.
This clause might say that the publisher will 'endeavour' to show the author's name on the cover, etc. This is not acceptable. They have the power actually to do it, and to make it a condition of any co-edition agreement. Make sure it does say it will be on the cover and title page - occasionally a publisher will miss your name off the cover, and some will even miss it off the title page. It is vitally important that you get your name on the title page as you need that in order to claim PLR in the book. If it is not mentioned in the contract, make sure you get it added. If you don't remember what PLR is, there is an earlier post on it and an article in the Bookseller about the importance of registering.
It is standard with licensed character work that your name will NOT be shown on the cover or title page, and you won't get this changed. The argument is that the book is usually presented as 'belonging' to the character (eg Angelina Ballerina's book of ballet shoes) and so it can't 'belong' to you. In addition, the character belongs to the original creator (which is a fair point) and they probably don't want your name on it. It is work for hire. There is nothing very imaginative in doing licensed character work - it follows a formula and adheres to a strict style and content guide. Accept that you won't get copyright or a cover/title page credit - if you don't like that, don't take the work. However, you may be able to get your name included on the imprint/acknowledgement page and as long as NO ONE has their name on the title page, you can still claim PLR on the book. It's worth arguing to have your name somewhere if it is a book that is likely to go into libraries (eg not a sticker book, or an activity book that is destroyed or defaced in use).
20**: the copyright date is always the date of first publication. If the book is reprinted in a later year, the copyright date stays the same. If the book comes out in a new edition, the copyright date changes when the text changes, but usually first copyright date is also shown.