Unlike relational database property of Strict consistency, eventual consistency property of a system ensures that any transaction will eventually (not immediately) bring the database from one valid state to another. This means there can be intermediate states that are not consistent between multiple nodes.
Eventually consistent systems are useful at scenarios where absolute consistency is not critical. For example in case of Twitter status update, if some users of the system do not see the latest status from a particular user its may not be very devastating for system.
Eventually consistent systems can not be used for use cases where absolute/strict consistency is required. For example a banking transactions system can not be using eventual consistency since it must consistently have the state of a transaction at any point of time. Your account balance should not show different amount if accessed from different ATM machines.