It means you don't have any warning that something will happen. Some examples: "be ready to go at a moment's notice" = be ready at any time - there will be no warning! "I'm ready to help at a moment's notice" = call me day or night, I'm here to help you! "Be ready to interview at a moment's notice" = you won't have any advance notification - be ready!

As in the sentence " be prepared to leave at a moment's notice." Literally one minute to.prepare to leave.

Rachel's answer is good. If someone gives you "notice," it means they tell you that something is going to happen. If I know that we will need to leave in one hour, I can give you an hour's notice that we will need to leave. Then you'll know that you need to be ready to leave in an hour. If I give my boss two weeks' notice that I am going to quit the job, then my boss has two weeks to find someone to replace me. "A moment's notice" means you will only be told about the event a moment before it happens. You will not have any time to prepare. Rachel gave some good example sentences. If you need to be ready "at a moment's notice," it means you need to get ready for the event in advance. If the event happens, it will happen suddenly, and there will be no time left to prepare. You will need to be prepared already.

it means "right away" or "without delay"

immediately when the time is right immediately when the time arrives For example: Let's prepare to take our mother to the hospital at a moment's notice = Let's prepare to take our mother to the hospital immediately when the time is right = Let's prepare to take our mother to the hospital when the time is right (when the time is right will depends on the context.) If your mother is sick, you may want to take her to the hospital when she asks you, so: You want to be prepared to take your mother to the hospital immediately when the time arrives. You want to be prepared to take your mother to the hospital when the time arrives. You want to be prepared to take your mother to the hospital when she tells you she is feeling worse. You want to be prepared to take your mother to the hospital the moment she tells you she is feeling worse. You want to be prepared to take your mother to the hospital at a moment's notice.