This anecdote takes place in chapter 7, during the all-important Ceremony of 12, when the 12-year-olds in the community receive their job assignments.
So far in the book we have learned that this society is like ours in many ways, but in other ways it's...different. Little by little Lowry adds in little tid-bits that reveal more and more important aspects of this dystopian society, and we should be getting more and more concerned.
The Chief Elder, the head of the community, gives a speech at this important event. Like many leaders in our world, she decides to sprinkle in a few funny stories. One of these is the story about how Asher used to confuse "snack" and "smack."
I think you'll agree, it's always funny when little kids mix up words, but that's not why Lowry has the Chief Elder share the story. First of all, we learn that kids are smacked with a wand when they mess up. Hopefully that's not like your school! So we learn that in this society it is very common for children to receive corporal punishment.
But the story even goes a step further! Little Asher would get smacked for messing up the word. He was just a kid! Can you imaging a kid being hit for getting a word wrong? Although the context of the story is supposed to be funny, you the reader should be off-put by it. The audience at the ceremony is laughing, but we shouldn't be. What kind of society is this? Why is hitting children something that's laughed at? If you've read on, you know that this is just the tip of the iceberg, but it's one of the many little warnings in the earlier part of the book that let us know that something is very wrong.