When typing AND, there is message that says to include at least one positive keyword with 3 characters

I would take it means to use AND after a word of at least three characters; it does not accept you use AND like first word.

I guess "and" is treated as a conjunction, and not as a word to search.

Agreed, the message is confusing. Take a look at this search page.

tagging and changing priority.

I guess that it should be explained better what positive word means, or that and is not considered.
Are there any other words with three or more characters that are not considered positive words?

The word "positive" there is rather hard to understand and should be removed.

OR is the only other word that is special, as far as I can see from the code.

You must include at least a keyword with 3 characters or more that is different from AND.

I agree that positive keyword is too difficult to be understood from all users, and is too generic. I take it means words without a particular meaning for the search engine, but that is not explicitly stated from the error message, which should report exactly which words are not considered.

OR is the only other word that is caught as a special case by the search engine -- might as well mention both of them. The 3 character limit is configurable, so someone could set it to 2.

Related issue:
#146278: The "No results" text is not correct for UserSearch -- search help needs to be per-plugin, not global

There are some other quirks of the search that definitely need to be mentioned. I think that this issue and #146278 are close enough to be considered duplicates. I'm moving the other one to be Drupal 7.x and adding some details to it, and I'm closing this one as a duplicate.