People were trying to understand what Jesus was about. The religious leaders were alarmed - he seemed to be associating with undesirables. Other people were puzzled - they had thought Jesus was associated with John the Baptist, but he didn't seem to be carrying on with the Baptist's style. And he certainly isn't behaving like an orthodox religious type. There's a sense of people grappling to find a precedent here, some way in which they can put Jesus in a pigeonhole, and understand him.
So first, a question about why he doesn't teach his disciples to fast, like John the Baptist did. Of course, this is hot on the heels of Levi's party, which probably didn't look a very holy affair.
Jesus's answer is given in terms of a celebration: if you've been invited to a wedding, you don't turn up dressed in black and refuse to eat at the reception, do you? One day the bridegroom will die, and then you'll mourn and fast.
Then he gives the illustration about not mending old clothes with unshrunk cloth, or pouring wine that's still fermenting into stiff old wineskins, that can't stretch any more. Both will end in disaster.
The message here seems to be that there is something new going on, and you can't come up with an old category to contain it. It will rip, it will tear, and this new thing will slip through your fingers.
You're going to have to be nimble in your thinking to keep up with Jesus - he's moving fast, and the old static thought processes can't match him.