This command displays the execution plan that the Postgres planner generates for the supplied query. The execution plan shows how the table(s) referenced by the query will be scanned---by plain sequential scan, index scan, etc.---and if multiple tables are referenced, what join algorithms will be used to bring together the required tuples from each input table.
The most critical part of the display is the estimated query execution cost, which is the planner's guess at how long it will take to run the query (measured in units of disk page fetches). Actually two numbers are shown: the start-up time before the first tuple can be returned, and the total time to return all the tuples. For most queries the total time is what matters, but in contexts such as an EXISTS sub-query the planner will choose the smallest start-up time instead of the smallest total time (since the executor will stop after getting one tuple, anyway). Also, if you limit the number of tuples to return with a LIMIT clause, the planner makes an appropriate interpolation between the endpoint costs to estimate which plan is really the cheapest.
The VERBOSE option emits the full internal representation of the plan tree, rather than just a summary (and sends it to the postmaster log file, too). Usually this option is only useful for debugging Postgres.
There is only sparse documentation on the optimizer's use of cost information in Postgres. General information on cost estimation for query optimization can be found in database textbooks. Refer to the Programmer's Guide in the chapters on indexes and the genetic query optimizer for more information.
To show a query plan for a simple query on a table with a single int4 column and 128 rows:
EXPLAIN SELECT * FROM foo;
NOTICE: QUERY PLAN:
Seq Scan on foo (cost=0.00..2.28 rows=128 width=4)
EXPLAIN
For the same table with an index to support an equijoin condition on the query, EXPLAIN will show a different plan:
EXPLAIN SELECT * FROM foo WHERE i = 4;
NOTICE: QUERY PLAN:
Index Scan using fi on foo (cost=0.00..0.42 rows=1 width=4)
EXPLAIN
And finally, for the same table with an index to support an equijoin condition on the query, EXPLAIN will show the following for a query using an aggregate function:
EXPLAIN SELECT sum(i) FROM foo WHERE i = 4;
NOTICE: QUERY PLAN:
Aggregate (cost=0.42..0.42 rows=1 width=4)
-> Index Scan using fi on foo (cost=0.00..0.42 rows=1 width=4)
Note that the specific numbers shown, and even the selected query strategy, may vary between Postgres releases due to planner improvements.