So far, the same result can also easily be achieved using sub-select. However, if you want more than just the overall average, sub-select will turn your queries into nightmares due to complexity. Suppose you don't just want the overall average but the average of the country you are dealing with. A PARTITION BY clause is what you need:

test=# SELECT country, year, production, consumption, 
              avg(production) OVER (PARTITION BY country) 
FROM t_oil; 
 country  | year  | production | consumption |      avg 
----------+-------+------------+-------------+-----------  
 Canada   | 1965  |   920      |     1108    | 2123.2173 
 Canada   | 2010  |   3332     |     2316    | 2123.2173 
 Canada   | 2009  |   3202     |     2190    | 2123.2173 
 ... 
 Iran     | 1966  |   2132     |     148     | 3631.6956 
 Iran     | 2010  |   4352     |     1874    | 3631.6956 
 Iran     | 2009  |   4249     |     2012    | 3631.6956 
 ... 

The point here is that each country will be assigned to the average of the country. The OVER clause defines the window we are looking at. In this case, the window is the country the row belongs to. In other words, the query returns the rows compared to all rows in this country.

Basically, a PARTITION BY clause takes any expression. Usually, most people will use a column to partition the data. Here is an example:

test=# SELECT year, production, 
              avg(production) OVER (PARTITION BY year < 1990)  
FROM  t_oil 
WHERE  country = 'Canada'  
ORDER  BY year; 
 year  | production |       avg 
-------+------------+----------------------- 
 1965  |        920 | 1631.6000000000000000 
 1966  |       1012 | 1631.6000000000000000 
 ... 
 1990  |       1967 | 2708.4761904761904762 
 1991  |        1983| 2708.4761904761904762 
 1992  |        2065| 2708.4761904761904762 
 ... 

The point is that data is split using an expression. year < 1990 can return two values: true or false. Depending on the group a year is in, it will be assigned to the pre-1990 average or to the post-1990 average. PostgreSQL is really flexible here. Using functions to determine group membership is not uncommon in real-world applications.