Examples of using the insert clause in CTE (with clause)

It is my first time learning CTE and I am a little confused with all the examples available on the internet. But with what I have read, I got these conclusion.

1. CTE is a temporary table (temporary table for us to look for what we want)
2. Since CTE is a temporary table, it essentially means that whatever "insert" we do to the main database is not equal to "insert" in CTE?

Please let me know what is wrong/right preferably with examples. I am very lost TT.