What is a session timeout?
This is a property that dictates how many seconds an availability replica waits for a (ping) response from another replica in the Availability Group considering the connection to have timed out and thus failed.
The default settings is set to ten seconds to wait for a ping response from a replica. This communication only occurs between the primary and secondary replicas.
Now, Microsoft does not recommend that you make this setting lower than ten seconds for fear that it will create a false alert of failure.
Why do I need it?
In situations where network latency is prevalent (especially considering across multi site Availability Groups), this might be a setting to look into. Many DBA's do not have control over the latency between data centers, a job that usually falls to the table of the Networking Team.
So to prevent false failures, you can look into increasing this setting.
This setting can be found by going to the properties of the availability group replica in SSMS:
Or with T-SQL:
ALTER AVAILABILITY GROUP <Ag_Name> MODIFY REPLICA ON '<instance_name> WITH (SESSION_TIMEOUT = 15);