This theme is at the core of "The Laboratory." It's the feeling that drives our speaker on her bloody quest. Basically, if she wasn't crazy jealous of her ex-lover and his new girlfriend, there wouldn't be a reason for this poem to exist. We get all kinds of hints throughout the poem that our speaker feels insanely jealous of other women, and would do almost anything to triumph over them. In that way, then, this poem can be seen as a kind of warning to readers about just how bad the times can be if jealously is allowed to fester unchecked.
The fire of the speaker's jealousy helps to make her actions seem more understandable. The poem uses the motivation of jealousy to lure us into seeing things her way. Spooky.
Browning uses this story to expose the ugly consequences of jealousy. He wants us to see how a little feeling of envy can snowball into something really terrible. Thanks for the heads up, Brownie!