A breakdown (without the dash) is a noun that has many meanings. Here are some I can think of:
something that fails or doesn't work: a breakdown in a relationship; the breakdown of a machine; a breakdown in talks between two governments
a point of mental exhaustion: an emotional breakdown; a mental breakdown
an explanation of information, esp. numbers/statistics: a breakdown of the numbers shows ....
a chemical change: the breakdown of a substance into smaller pieces or parts
There are probably more than these meanings.
"Broken-down" (with a dash) is an adjective: the broken-down house