Dynamic sampling (DS) was introduced in Oracle Database 9i Release 2 to improve the optimizer's ability to generate good execution plans. The most common misconception is that DS can be used as a substitute for optimizer statistics. The goal of DS is to augment the optimizer statistics; it is used when regular statistics are not sufficient to get good quality cardinality estimates.
So how and when will DS be use? During the compilation of a SQL statement, the optimizer decides whether to use DS or not by considering whether the available statistics are sufficient to generate a good execution plan. If the available statistics are not enough, dynamic sampling will be used. It is typically used to compensate for missing or insufficient statistics that would otherwise lead to a very bad plan. For the case where one or more of the tables in the query does not have statistics, DS is used by the optimizer to gather basic statistics on these tables before optimizing the statement. The statistics gathered in this case are not as high a quality or as complete as the statistics gathered using the DBMS_STATS package. This trade off is made to limit the impact on the compile time of the statement.
The second scenario where DS is used is when the statement contains a complex predicate expression and extended statistics are not available. Extended statistics were introduced in Oracle Database 11g Release 1 with the goal to help the optimizer get good quality cardinality estimates for complex predicate expressions. For example, if you had a simple query that has where clause predicates on two correlated columns, standard statistics would not be sufficient.