A pun is described as playing with words.
Drilling for oil is boring.
Boring can mean being fed up, or it can mean drilling a hole. This pun mixes those meanings up.

Sometimes a pun uses a word, because, when spoken it can sound a bit like something else.
In the Canadian forests, it's sometimes hard to cedar wood for the trees
Here 'cedar' sounds rather like 'see the' in the common phrase.

In this case, the dogs name has been chosen to complete the word 'badminton', the game you play using shuttlecocks!
My dog Minton just ate two of my expensive shuttlecocks!
"Bad Minton!"

Here are some other puns. If you don't understand what the joke is, trying saying them out loud first and then ask your teacher.