What it is
The only thing that teething reliably produces is a tooth. Sometimes several teeth at once, but all the symptoms we usually attribute to teething may or may not be because of the tooth coming in.
If you think about it, the kids are probably always teething-the teeth have to come from somewhere, so there are probably teeth moving around all the time. But, for discussion sake, we will talk about "teething" as the days immediately before and the day of tooth eruption from the gum.
If your child is about 3-4 months old and you are reading this, your child is probably drooling like a big dog and trying to stuff their whole hand in their mouth. This is really common and I'm not sure it means teething. The kids are trying to figure out what their hands are all about and the only way to do that is to get them to the place that can give them the most information- their mouth. If you are sampling the world with your tongue, you drool like a big dog, but if you are going to figure out what is new in your world, especially how to use your hands, then you need to try to bite your fists.
That having been said, teething can happen pretty much at any time. Some kids are born with teeth and some don't have any at a year of age. You need at lest 1 by 18 months. And they are supposed to come in front first, but as always, they haven't read the book, so they can come in any way they want. Within reason I guess.
What it isn't
A serious illness. So before we going and chalking up bad symptoms to "teething" we ought to explore other possibilities.
The ancient Sumerians believe that teething and being infested with worms were related. And even smart people like Aristotle thought that teething was associated with serious childhood illness.
OK-I have a big list. But, no symptoms occur in more than about 1/3rd of kids in any studies done. Meaning, none of these are perfect symptoms to tell if your child is teething.
Associated: biting, drooling, gum-rubbing, irritability, sucking, sleep awakenings, ear-rubbing, decreased solid food appetite, and maybe a fever but less than 101.
Not associated: Diarrhea (maybe, if it's related, it's weakly related), congestion, increased stool number, cough, vomiting and fever over 102.
I'm not a big fan of the Orajel and other mouth-numbing products, mainly because they can numb everything they come in contact with, including the protective airway reflexes of the child's mouth. Tylenol works, but it's not much of an anti-inflammatory, so I have been recommending Ibuprofen (like Advil or Motrin) in children over 6 months because these products are anti-inflammatory as well as pain relieving. Tylenol should be used in children under 6 months.