OPTIMIZER MODE in Oracle

                ALL_ROWS   : The optimizer will attempt to find an execution plan that completes the statement (typically meaning “returns all the rows”) in the shortest possible time. There are no special constraints built into this code. Used typically in OLAP Systems.

                FIRST_ROWS_N (N => 1, 10,100,1000) The optimizer first estimates the number of rows that will be returned by completely analyzing just the first join order. This tells it what fraction of the total data set the query is supposed to fetch, and it restarts the entire optimization process with the target of finding the execution plan that minimizes the resources required to return that fraction of the total data. This option was introduced in 9i. Used typically in OLTP systems.

                FIRST_ROWS:  Deprecated in 9i, but maintained for backward compatibility. The optimizer will attempt to find an execution plan to return the first row of a result set as rapidly as possible. There are several high-level constraints built into the code.

There are two other options for the optimizer_mode (even in 10g): rule and choose (default).

Up to Oracle9i, the default value is choose. This means that if object statistics are available for at least one of the objects referenced in the SQL statement that has to be optimized, the value all_rows is used; otherwise, rule is used.

As of Oracle Database 10g, the rule-based optimizer has been desupported , and therefore the new default value is all_rows. Consequently, the values choose and rule are no longer supported

Any tables that missed the most recent pass of statistics generation will then be subject to dynamic sampling. This is because the default value in 10g for the parameter optimizer_dynamic_sampling is 2 (which means use dynamic sampling on any table without statistics), rather than 1, as it was in 9i. 

Courtesy  : CBO Fundamentals by Johnathan Lewis and Troubleshooting Oracle Performance  by Christian Antognini