What does it mean Include inherited columns?
ServiceNow enables to specify a parent for a table. It means all the columns in the parent table are used for the child table as well. For example the table task (parent) and incident (child). Many tables are derived from the task table. The whole CMDB is build on this inheritance design pattern. Etc.
SnowMirror enables two approaches when synchronizing inherited tables (e.g. incident)
1) Synchronize two tables. This is the way ServiceNow itself stores the data. You have to synchronize two tables (e.g. task and incident) and to obtain the incident record you have to join the tables using the sys_id primary key in both tables. The advantage of this approach is lower redundancy. If you are synchronizing several tables derived from the task table the situation is simpler to perform some type of queries.
2) Synchronize only one table with all parent inherited columns included. This is an approach that a typical user expects. To sync the data as it is displayed in the web application. Check the checkbox Include inherited columns in the synchronization settings to choose this approach.