How group by and having Queries with Aggregates Work

The where clause excludes rows that do not meet its search conditions; its function remains the same for grouped or nongrouped queries.

The group by clause collects the remaining rows into one group for each unique value in the group by expression. Omitting group by creates a single group for the whole table.

Aggregate functions specified in the select list calculate summary values for each group. For scalar aggregates, there is only one value for the table. Vector aggregates calculate values for the distinct groups.

The having clause excludes groups from the results that do not meet its search conditions. Even though the having clause tests only rows, the presence or absence of a group by clause may make it appear to be operating on groups:

When the query includes group by, having excludes result group rows. This is why having seems to operate on groups.
When the query has no group by, having excludes result rows from the (single-group) table. This is why having seems to operate on rows (the results are similar to where clause results).