Prime lenses are excellent options for portrait work, especially at wedding venues. Prime lenses are less forgiving when it comes to varied situations and framing. Instead of moving the zoom ring, you have to move your feet. If you are the main photographer for an event, no one is going to mind you moving around to get the shot. If you are an audience member attending the wedding as a guest, it may be considered rude to get move around so much for a shot.
Typically indoor weddings have poor lighting, at both the ceremony and reception events. Because of that, fast lenses of at least f/2.8 are usually the standard. You could fill your gear bag with zoom lenses at f/2.8, and shoot weddings very well, but it would likely be less expensive to purchase a few f/1.4, f/1.8 or f/2.0 lenses that are wider yet.
Another benefit of prime lenses is that typically they are smaller and lighter then a professional grade zoom lens.
For portraits specifically, a wider aperture will provide you with a more blurred background, referred to as bokeh. It also will let you stop action such as a moving bride or groom, and allow you to use a lower ISO setting if you are worried about noise.
Overall, prime lenses are a great option for wedding photography, because they are particularly good at portrait work, especially in low light.
To get started these questions may help you with your first purchase: