A place that's so packed with people that it's unsafe or unhealthy is overcrowded. If the subway is overcrowded after the big concert, you should probably wait for the next one.
If your party is bustling with guests, it's crowded. But if each of your friends invited all their family members to come along, it's overcrowded. In some cases, too many people being present means a shortage of resources, like in an overcrowded school or hospital. An overcrowded club or concert is dangerous because people are at risk of being injured during an emergency exit. Crowded is from a root meaning "to press or push," and over means "beyond."