A site does not "need" them, but it is preferable to have them. Robots is the term used for the web bots/spiders that crawl web sites cataloguing them for the search engines. Using meta tags such as you cited instructs these spiders whether to index (add) the web page to their listing, and whether to follow links they find on that page.
The correct way to control this behaviour is to use a robots.txt file in the root folder, containing all the instructions about which spiders may or not crawl the site, about which folders and file types it may access or index. This can then be augmented by those meta tags to vary the general rules for individual pages.