If a thing falls apart, it breaks into pieces; if a person falls apart, they start crying, screaming, become hysterical - and this can happen at once or over time: (1) When she walked up to the crowd on the street and realized her dog had been hit by a car, she fell apart and had to be taken home. (2) After her divorce she just fell apart; she started drinking, stopped hanging out with her friends, paid little attention to her children and neglected her work.

If you give me the context you saw this in, I can clarify it for you.