How to check the maximum number of allowed connections to an Oracle database?

The sessions parameter is derived from the processes parameter and changes accordingly when you change the number of max processes. See the Oracle docs for further info.

To get only the info about the sessions:

    select current_utilization, limit_value 
    from v$resource_limit 
    where resource_name='sessions';

CURRENT_UTILIZATION LIMIT_VALUE
------------------- -----------
                110         792

Try this to show info about both:

    select resource_name, current_utilization, max_utilization, limit_value 
    from v$resource_limit 
    where resource_name in ('sessions', 'processes');

RESOURCE_NAME CURRENT_UTILIZATION MAX_UTILIZATION LIMIT_VALUE
------------- ------------------- --------------- -----------
processes                      96             309         500
sessions                      104             323         792