“Images on this site may not be used without my express written permission.”
You have a website where you post photographs that you've taken. You don't want people to take your photos and use them on other web sites without asking you, so you write this at the bottom of the page.
Images on this site may not be used without my express written permission.
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use images
"Images" means "pictures". But while "pictures" suggests photographs specifically, "images" can mean photos, illustrations, charts, etc. as well.
To "use" images means to publish them, put them in a website, print them, and so on.
a site
"A site" means a website.
(something) may not be (done)
This is a formal way of telling people something that they can't do:
School computers may not be used for playing games or surfing the Internet.
Items may not be returned after 30 days.
You speak or write this way if you're the one in charge of something.
(someone's) express written permission
Getting someone's "express permission" means clearly and specifically getting their permission to do something.
Sometimes it's OK to do something without getting express permission for it. For example, if you are renting an apartment you can probably hang a small picture on the wall without asking your landlord. But if you want to install new kitchen cabinets, you will need to get your landlord's express permission.
This is a formal and legal-sounding phrase.
The word "express" is also used as an adjective to mean "specific" in this phrase:
I came here for the express purpose of finding a job.