In "Lamb to the Slaughter", why does Mary giggle at the end of the story?

This excellent short story is usually used by teachers to
demonstrate irony. Of course, as you know, there are three types of irony - verbal,
situational and dramatic. The answer to your question is related to dramatic irony,
which is defined as  when the reader and some of the characters involved in a play or
text know something important that some or all of the characters do not know. What is
darkly comic about the ending is the dramatic irony that we as readers are privileged to
know. Mary Maloney has just killed her husband, then has calculatedly managed to give
herself an alibi and then get rid of the murder weapon. Of course, the policemen
unwittingly help Mary get away with it:

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"Personally, I think [the murder weapon] is
right here on the premises."

"Probably right under our very
noses. What you think, Jack?"

And in the other room, Mary
Maloney began to giggle.

The
murder weapon was indeed "right under their very noses", but they were just enjoying the
meal. Given the emphasis that is placed on finding the murder weapon, ("It's the old
story. Get the weapon and you've got the man"), the fact that Mary manages to trick the
policemen into eating it, thereby ensuring herself her "innocence", ends this darkly
humorous tale.