It means "this one or that one." This is used in positive sentences. Positive sentences are the sentences that do not have any "not or no or etc."
It means "not this one nor that one." It is used in negative sentences.
When we use Either...or and Neither..nor, we should pay attention to two points:
1- The parallel structure should be used after these words.
For example: Many people drink neither coffee nor alcohol.
Coffe and alcohol are both nouns. We can not use noun in one part of the sentence and adjectives in the other. We should use both nouns or adjectives or verbs in both part of the sentence.
In fact, the original sentence was: Many people don't drink coffe. Many people don't drink alcohol.
So, we connected these two sentences together with the help of Neither...nor.
2-Another point that we should consider while using these is verb and subject agreement.In these sentences, verb should agree with the closest noun. If the noun is single, we use single verb. If not, we use plural verb.
for example: Neither the students nor the teacher knows the answer.
In this sentence, teacher is the closest noun to the verb. It is single so, we use single verb which is knows.
For more practice, I will add some excersices here. You can practice them and if you have any question, please feel free to ask. I will be glad to help.
Here is the practice:
Combine the following sentences into sentences which contain parallel structure:
1-Barbara is fluent in Chinese. She is also fluent in Japanese. (not only..but also)
2-If you want to change your class schedule, you should talk to your teacher, or you should talk to your academic counselor.(either...or)
3-Michael didn't tell his mother about the trouble he had gotten into. He didn't tell his father about the trouble he had gotten into. (neither...nor)
Use appropriate verb form for filling these sentences:
1-Neither Alan nor Carol............to go skiing this weekend.(want)
2-Either Jack or Alice.............the information you need.(have)
3-Neither my parents nor my brother.........with my decision.(agree)