Broca was interested in how damage to the brain affected people.
One famous case was dealt with a man named "Tan". He was called this because that is all he could say. After the man died, Broca performed an autopsy and found a portion of the man's frontal cortex on the left side to be damaged by a lesion.
From studying Tan's brain, and other like him, Broca found that that specific area of the brain had control over the expression of language. The people with damage to this area can still read and write, but have trouble verbalizing. This area is now called Broca's area.