To merge features based on specified attributes.
A dissolve merges smaller features into larger features based on common specified attributes. For example combining city district polygons into a single city polygon, based on a city name attribute.
Dissolve is an aggregation of geometry based on a common attribute, but may or may not aggregate other attribute values depending on use and implementation. Also, features may not require adjacency to be merged, and multi-part features can be created.
The help page on How Dissolve works in ArcGIS 10.1 provides graphic examples.