Re-Index deletes existing content from the Index Store and then re-indexes everything.
Re-Indexing is done as part of search crawler(s) scheduled job. The search crawler(s) should be run manually under Host > Schedule to re-index immediately. Re-indexing is done for the current site only.
Caution - This should be done during non-peak hours as the process can be CPU intensive.
Many times when searching for something users don't know exactly what they are looking for and so they look for words that are synonymous in hopes of finding the term. This feature allows you to create those synonymous relationships between terms.
When performing a search we want to avoid certain words that may decrease the value of the search results. This feature allows you to add words that will be ignored by search queries.