PostgreSQL makes its decisions about how queries execute based on
statistics collected about each table in your database. This information
is collected by analyzing the tables, either with the ANALYZE statement or via autovacuum doing that step. In either case, the amount of information collected during the analyze step is set by default_statistics_target. Increasing this value makes analysis take longer, and as analysis of autovacuum
happens regularly this turns into increased background overhead for
database maintenance. But if there aren't enough statistics about a
table, you can get bad plans for queries against it.
The default value for this setting used to be the very low (that is,10), but was increased to 100 in PostgreSQL 8.4. Using that larger value was popular in earlier versions, too, for general improved query behavior. Indexes using the LIKE operator tended to work much better with values greater than 100 rather than below it, due to a hard-coded change at that threshold.
Note that increasing this value does result in a net slowdown on your system if you're not ever running queries where the additional statistics result in a change to a better query plan. This is one reason why some simple benchmarks show PostgreSQL 8.4 as slightly slower than 8.3 at default parameters for each, and in some cases you might return an 8.4 install to a smaller setting. Extremely large settings for default_statistics_target are discouraged due to the large overhead they incur.
If there is just a particular column in a table you know that needs better statistics, you can use ALTER TABLE SET STATISTICS on that column to adjust this setting just for it. This works better than increasing the system-wide default and making every table pay for that requirement. Typically, the columns that really require a lot more statistics to work properly will require a setting near the maximum of 1000 (increased to 10,000 in later versions) to get a serious behavior change, which is far higher than you'd want to collect data for on every table in the database