The Segment operator, like all operators, is described at the Books Online page mentioned above. Here is the description, quoted verbatim:
Segment is a physical and a logical operator. It divides the input set into segments based on the value of one or more columns. These columns are shown as arguments in the Segment operator. The operator then outputs one segment at a time.
Looking at the properties of the Segment operator, we do indeed see the argument mentioned in this description, in the Group By property (highlighted in the screenshot). So this operator reads the data returned by the Index Scan (sorted by TerritoryID, which is required for it to work; this is why the Index Scan operator is ordered to perform an ordered scan), and divides it into segments based on this column. In other words, this operator is a direct implementation of the PARTITION BY spefication. Every segment returned by the operator is what we would call a partition for the ROW_NUMBER() function in the T-SQL query. And this enables the Sequence Project operator to reset its counters and start at 1 for every new segment / partition.
Read on to understand the issue and see Hugo’s proof.