"Giving an update" means telling someone the newest information about something.
For example, if you're working on a project at work, your boss might ask you to give her an update every day or two. Your update will include information about how soon you will be done, what problems you've had, and so on.
You can also use "update" as a verb:
Please update Jana if anything changes.
But "update" as a verb is more formal than "give (someone) an update". It sounds a little like military speak.