Concurrent Sessions normally refers to maximum simultaneous connection from clients that ASA can handle. Each ASA model has different capacity to handle this connections.
New Sessions per second refers to how many new connections from clients can be accepted by ASA.
depends model you need to look feature of the product. this means if the concurrent session max out, new session will not be established, it start dropping the sesssion, until old session terminatied from sessions.
make sense ?