Emblems are basically an old rewards system of PC's. You could get one for various reasons, such as hitting a posting milestone, for your birthday, winning an event, among many others. Staff members manually handed them out to people. Some you could request. The likely reason you don't have an emblems tab on your profile page is because you probably don't have any emblems.
It's kind of a dead feature now, although we have been very slowly getting around to replacing it with something a little better. When will this thing be implemented? idk