Prior to the key quote cited above, romantically frustrated, Margaret, had been fighting with her husband, Brick, about past affairs and why he doesn't show her affection anymore. Throughout the play, scandalous and often important secrets are kept from various members of the family, from Big Daddy's fatal illness to the real reason Brick became an alcoholic and lost all affection for Margaret. Williams, being a controversial writer, slowly starts to later bring these issues to light, just as his intentions are in getting the theme across. The whole play is spent establishing secrets with the reader that are driving the characters to be so distressed, but none of the characters know truly, which is what the quote suggests in relation to the text. The secrets are ruining relationships and "festering" inside each character, eating them alive with guilt. Just like the universal metaphor of the "cat on a hot tin roof", this quote compares one of the text's central ideas to being burned. Keeping the truth secret is only torment to a smart soul.
The work's true essential reality is the presence of the all-natural truth. If one chooses to hide the truth, the one and all parties involved will end up burned, no matter the controversy.