The feature only appears when you aren't in a guild, taking the place of the usual "you aren't in a guild" message you get when you're guildless on live realms.
Overall, the feature looks a bit too simplified for serious raiding or PvP guilds, but for anyone looking for a casual, social, or leveling guild, this new feature seems like a great way to ease the guild search.
Currently, there don't appear to be any guilds in the "Browse Guilds" tab, but based on the grayed-out option to "Request Membership," I'm thinking guild leaders have to set up recruitment status on their end. I guess we'll have to wait for Guild Master Holisky to charter the guild so we can see just how much information a guild can feature on this tab.
We'll keep you up to date as we learn more.
Update: After chartering a guild I've found that there are currently no recruitment options available to a guild leader inside the guild or social panels. This probably means Blizzard hasn't finished implementing the feature yet. Stay tuned!