Generally, making database changes is absolutely the wrong thing to do. You should never touch a Jira database unless you are fixing something, and you are 100% sure you understand what you are doing. The fact you are asking this question tells me that you do not understand.
Anyway, to answer the actual question: Jira caches and indexes things. You must never write to a running Jira database because both of those things can scrub your changes, corrupt your data and leave you with an unusable Jira.
If you must make SQL changes, then
Always stop Jira. No question of this, even tricks that flush caches fail a lot. Always, always, always stop Jira.
For indexing: you need to understand what is indexed in order to decide whether to re-index afterwards (if you've touched an issue, project, user or scheme, you should always re-index. Other stuff - there's a 90% chance you need to), but the general rule is "if in doubt, do a full, locking re-index".
Always back up the database, and prove that the backup is restore-able before running the SQL and restarting
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