Any intelligent person can understand the characteristics of an avatāra by understanding two features—the principal feature, called personality, and the marginal features. In the scriptures there are descriptions of the characteristics of the body and the activities of an incarnation, and the description of the body is the principal feature by which an incarnation can be identified. The activities of the incarnation are the marginal features. This is confirmed in the beginning of Śrīmad-Bhāgavatam (1.1.1) where the features of an avatāra are nicely described. In that verse, the two terms param and satyam are used, and Lord Caitanya indicates that these words reveal Kṛṣṇa's principal feature. The other marginal features indicate that He taught Vedic knowledge to Brahmā and incarnated as the puruṣa-avatāra to create the cosmic manifestation. These are occasional features manifest for some special purposes. One should be able to understand and distinguish the principal and marginal features of an avatāra. No one can declare himself an incarnation without referring to these two features. An intelligent man will not accept anyone as an avatāra without studying the principal and marginal features. When Sanātana Gosvāmī tried to confirm Lord Caitanya's personal characteristics as being those of the incarnation of this age, Lord Caitanya Himself indirectly made the confirmation by simply saying, "Let us leave aside all these discussions and continue with a description of the śaktyāveśa-avatāras."
The Lord then pointed out that there is no limit to the śaktyāveśa-avatāras and that they cannot be counted. However, some can be mentioned as examples. The śaktyāveśa incarnations are of two kinds—direct and indirect. When the Lord Himself comes, He is called sākṣāt, or a direct śaktyāveśa-avatāra, and when He empowers some living entity to represent Him that living entity is called an indirect or āveśa incarnation. Examples of indirect avatāras are the four Kumāras, Nārada, Pṛthu and Paraśurāma. These are actually living entities, but there is specific power given to them by the Supreme Personality of Godhead. When a specific opulence of the Supreme Lord is invested in specific entities, they are called āveśa-avatāras. The four Kumāras specifically represent the Supreme Lord's opulence of knowledge. Nārada represents the devotional service of the Supreme Lord. Devotional service is also represented by Lord Caitanya, who is considered to be the full representation of devotional service. In Brahmā the opulence of creative power is invested, and in King Pṛthu the power for maintaining the living entities is invested. Similarly, in Paraśurāma the power for killing evil elements is invested. As far as vibhāti, or the special favor of the Supreme Personality of Godhead, is concerned, it is described in the Tenth Chapter of Bhagavad-gītā that a living entity who appears to be especially powerful or beautiful should be known to be especially favored by the Supreme Lord.
Examples of direct or sākṣād-avatāras are the Śeṣa incarnation and the Ananta incarnation. In Ananta the power for sustaining all planets is invested, and in the Śeṣa incarnation the power for serving the Supreme Lord is invested.