Enjoying that special moment. Being able to enjoy and savor that first moment of seeing one another on your wedding day in an intimate setting... Without all your guests watching. Being able to hug/kiss/cry/laugh/smile and not feel like you have to hold back. Having that instant reaction and tender moment documented. its the ONLY alone time you will have during your wedding day. 
Timing. Doing a First Look provides much more time for photos without being rushed. Immediately after the First Look, I typically photograph the bride and groom together for a little while. Then I photograph the bridal party (the bridal party can meet the bride and groom at First Look location or wait in transportation until First Look and bride/groom photos are complete.) Family photos can even be done before the ceremony as well. Then after the ceremony, I usually do family photos if they have not been done already and additional photos of the bride/groom and sometimes more of the bridal party if time allows it. 
Attending Cocktail Hour. This ties into timing, but when we do the majority of photos before the cocktail hour, couples can attend some if not all of their cocktail hour. Doing a First Look and photos before the ceremony often allows for much flexibility and options with the wedding day timeline and photo opportunities. 
Daylight. Depending on what time of year a wedding is or how late the ceremony starts, a First Look enables the couple to have beautiful natural light photos while it is still light outside. If a couple is getting married in November on the east coast with an evening ceremony at 7:00pm, it will obviously be pitch dark outside when the ceremony is done. Doing a First Look, bride/groom photos, bridal party photos, and even family photos prior to the ceremony and sunset would allow for photos outside in the beautiful light... 
Calming those nerves. My brides are definitely less nervous for the ceremony and the rest of the wedding day when they do a First Look. They are just as excited and anxious, as are the grooms, but less nervous since they have already had time with their soul mate before the ceremony. One of my brides described it best when she told me that the First Look and walking down the aisle were two completely different experiences, but just as emotional and exciting. Walking down the aisle was something she had always dreamed about and the First Look was something she had been looking forward to in the year leading up to the wedding when they decided to do a First Look. And I will tell you that their First Look and walk down the aisle were so incredibly beautiful and emotional in their own way.