Why does google appear in Firefox search bar

Because people usually want something to search with — depending on your region there might be better options, see Manage my default search engines in Firefox for Android if anything suits you better.

Why does google appear in Firefox search bar?

Because that is the search engine you have set to use on the Firefox for Android web browser.

Firefox for Android is a web browser and not a search engine site. Mozilla the makers of the Firefox web browsers does not have a search engine site of their own.