Hi and welcome to the forum.
In some cases, we use the "o-"
honorific to indicate who an item belongs to. For example, when referring to my beer and your beer, I might say, "obi-ru" when referring to your beer, but similarly only saying, "bi-ru" when referring to my own beer. (This has the added effect of eliminating the need to say, "my—" and "your—", because in some cases, saying 'your' and 'my' in Japanese can be a bit tricky.) In this way, a waitress asks, "Obi-ru desu ka?" to ask if you want a beer. (The idea is, your beer is 'honorable' whereas mine is not.)