This phrase was easy to track down on the internet. It means “a course of action with inevitable bad consequences has begun. The allusion to fat dropping into a fire and causing a burst of flames was already a proverb in John Heywood’s 1546 collection.” (dictionary.com)
Times of India adds that “in its earliest use (14th century), the expression had to do with failure; only later did it come to imply, as it now does, a crisis or an explosion of anger, recrimination or trouble.”
The phrase originated when fat was valued – I suppose a modern dieter might want fat to burned off!