The phrase in conclusion can be used at the end of a speech or essay, and it means "to sum things up" or "finally." In conclusion, it’s a very handy phrase for formal speaking and writing.
There are other ways to finish up a paper or oral report, but in conclusion makes it clear that you're getting close to the end, and it reminds your audience of what your main idea or thesis is. It’s a type of transitional word, which are words such as first, next, or finally. Transitional words are like bridges between thoughts. The word conclusion comes from the Latin concludere, which combines con-, "completely," and claudere, "to shut."