What is the definition of "pet" openings?

Any opening that is a players favorite.

My cat is an e4 player.

It has to meet at least 3 of the following 5 criteria:

○ Knows a few tricks
○ Wears a collar
○ Luxurious fur coat
○ 4 legs
○ Wagging tail

(I might be thinking of dogs though)

Ha!

Wait til cottonsock sees this...

A pet opening usually refers to someone's favourite opening/variation of an opening, one that he or she plays very often given the chance, and it generally entails some degree of obscurity.  You generally don't say the Sicilian is your pet opening against 1.e4, for example, but the 2...Nf6 Sicilian would be.

Sort of...

it usually also implies that the person has studied it in depth, and has a lot of experience playing it...

They've spent more time with it than other openings... maybe that's a good way to say it.

And while I'm not sure obscurity is necessary, that usually seems to be the case.

You wouldn't say, for example, that the Najdorf itself is a pet line, but a particular line of the Najdorf a player chooses on move 10 or 15 or something might be called a pet line.

Think of it this way: every player has an opening repertoire.  Some are in depth, some end after two moves, but there is at least a general idea of what to do in a given opening.  For example:

Against 1...e5 I play the Italian, against 1...c5 the Alapin, against the French and Caro-Kann the Exchange, etc.  This is your repertoire.

You wouldn't say the Italian is your 'pet' opening, because everyone plays and knows the Italian.  More accurately, you could say you are an Italian specialist; you specialize in a certain opening, playing it a lot and knowing the ins and outs.

What makes it a pet opening, in my view, is some level of obscurity.  For instance, if you played the Scandinavian as White by playing Nc3, Nf3, Bc4, etc, that's just normal development.  If instead you played something with a twist, you could have your pet system against that opening.

You could have many pet openings; you could have one for every major variation, and some amateurs have done just that, crafting off-beat and tricky variations.  This can be extremely strong in blitz.  It's also not an area you should invest too much time in, but it's undeniably fun.