In sports betting, the term "puppy" refers to when a team is an underdog, meaning that they are not favoured to win.
To get more specific, a "puppy" usually refers to a team that is a small underdog.
Chelsea, 5/4
Draw, 3/1
Manchester United, 2/1
In this case, Chelsea is a very small underdog, as they are listed at 5/4. In fact, none of the three betting options are better than even money to win.
Chelsea could be called a "puppy" in this case, as they are a very small underdog.
The term "puppy" isn't used very much, as most people prefer to say "small underdog" instead.