In order to have a robotic system able to effectively learn by imitation, and not merely reproduce the movements of a human teacher, the system should have the capabilities of deeply understanding the perceived actions to be imitated. This paper deals with the development of cognitive architecture for learning by imitation in which a rich conceptual representation of the observed actions is built. The purpose of the following discussion is to show how this Conceptual Area can be employed to efficiently organize perceptual data, to learn movement primitives from human demonstration and to generate complex actions by combining and sequencing simpler ones. The proposed architecture has been tested on a robotic system composed of a PUMA 200 industrial manipulator and an anthropomorphic robotic hand.