Hi Sumesh,
1. Concurrent Sessions means number of simultaneous sessions at any given time. For ex. For ASA 5512-X support 100,000 concurrent sessions, this means up to 100,000 sessions can be handled.
2. Half-opened Connections: It is a TCP connections whose state is out of synchronization between the two communicating hosts, possibly due to a crash of one side. The term half-open connection is most often used to describe an embryonic connection, i.e. a TCP connection which is in the process of being established.
3. Half-Closed Connection: TCP provides the ability for one end of the connection to terminate its output, while still receiving data from the other end. This is called a half-close.