2 per second indicates that the application is not correctly using connection pooling.
What does Application is not correctly using the connection pooling -- What does it mean ?
From the Documentation for this counter..
Logins/sec Total number of logins started per second. This does not include pooled connections.
So you need not worry about connection pooling reusability..
I am not able to connect the link between the Logins/sec and session ids
This has been answered by Remus Rusanu here :What is the difference between a connection and a session? ,normally connection and session have one to one mapping..
The connection is the physical communication channel between SQL Server and the application: the TCP socket, the named pipe, the shared memory region. The session in SQL Server corresponds to the Wikipedia definition of a session: a semi-permanent container of state for an information exchange. In other words the sessions stores settings like cache of your login information, current transaction isolation level, session level SET values etc etc.
Normally there is one session on each connection, but there could be multiple session on a single connection (Multiple Active Result Sets, MARS) and there are sessions that have no connection (SSB activated procedures, system sessions). There are also connections w/o sessions, namely connections used for non-TDS purposes, like database mirroring sys.dm_db_mirroring_connections or Service Broker connections sys.dm_broker_connections.
To Practice and understand more on this,this link helped me,you can take a look..