Like most other relational database products, PostgreSQL supports aggregate functions. An aggregate function computes a single result from multiple input rows. For example, there are aggregates to compute the count, sum, avg (average), max (maximum) and min (minimum) over a set of rows.
As an example, we can find the highest low-temperature reading anywhere with
SELECT max(temp_lo) FROM weather;
max ----- 46 (1 row)
SELECT city FROM weather WHERE temp_lo = max(temp_lo); WRONG
but this will not work since the aggregate max cannot be used in the WHERE clause. (This restriction exists because the WHERE clause determines the rows that will go into the aggregation stage; so it has to be evaluated before aggregate functions are computed.) However, as is often the case the query can be restated to accomplish the intended result, here by using a subquery:
SELECT city FROM weather WHERE temp_lo = (SELECT max(temp_lo) FROM weather);
city --------------- San Francisco (1 row)
This is OK because the subquery is an independent computation that computes its own aggregate separately from what is happening in the outer query.
SELECT city, max(temp_lo) FROM weather GROUP BY city;
city | max ---------------+----- Hayward | 37 San Francisco | 46 (2 rows)
which gives us one output row per city. Each aggregate result is computed over the table rows matching that city. We can filter these grouped rows using HAVING:
SELECT city, max(temp_lo) FROM weather GROUP BY city HAVING max(temp_lo) < 40;
city | max ---------+----- Hayward | 37 (1 row)
which gives us the same results for only the cities that have all temp_lo values below 40. Finally, if we only care about cities whose names begin with "S", we might do
SELECT city, max(temp_lo) FROM weather WHERE city LIKE 'S%'(1) GROUP BY city HAVING max(temp_lo) < 40;
It is important to understand the interaction between aggregates and SQL's WHERE and HAVING clauses. The fundamental difference between WHERE and HAVING is this: WHERE selects input rows before groups and aggregates are computed (thus, it controls which rows go into the aggregate computation), whereas HAVING selects group rows after groups and aggregates are computed. Thus, the WHERE clause must not contain aggregate functions; it makes no sense to try to use an aggregate to determine which rows will be inputs to the aggregates. On the other hand, HAVING clauses always contain aggregate functions. (Strictly speaking, you are allowed to write a HAVING clause that doesn't use aggregates, but it's wasteful: The same condition could be used more efficiently at the WHERE stage.)
Observe that we can apply the city name restriction in WHERE, since it needs no aggregate. This is more efficient than adding the restriction to HAVING, because we avoid doing the grouping and aggregate calculations for all rows that fail the WHERE check.