The Group tab on the query canvas represents the Group By section (SQL clause) of your query.
This allows you specify which columns you wish to group by when using aggregate functions.
For example, if you were showing all sales by sales category name, you would be selecting the category name column and using the sum() aggregate function on the TotalSales column, and on the Group tab you would have the category name column to indicate this is how you would like to group.
The With Rollup option can be used when you wish to group by more than one column. This allows you to create a result table with totals and sub-totals.
You can find out more about the Group By clause here.
You can find out more about With Rollup here.