SB 10.46.1

śrī-śuka uvāca
vṛṣṇīnāṁ pravaro mantrī
 kṛṣṇasya dayitaḥ sakhā
śiṣyo bṛhaspateḥ sākṣād
 uddhavo buddhi-sattamaḥ
Synonyms: 
śrī-śukaḥ uvāca — Śukadeva Gosvāmī said; vṛṣṇīnām — of the Vṛṣṇis; pravaraḥ — the best; mantrī — adviser; kṛṣṇasya — of Kṛṣṇa; dayitaḥ — beloved; sakhā — friend; śiṣyaḥ — disciple; bṛhaspateḥ — of Bṛhaspati, the spiritual master of the demigods; sākṣāt — directly; uddhavaḥ — Uddhava; buddhi — having intelligence; sat-tamaḥ — of the highest quality.
Translation: 
Śukadeva Gosvāmī said: The supremely intelligent Uddhava was the best counselor of the Vṛṣṇi dynasty, a beloved friend of Lord Śrī Kṛṣṇa and a direct disciple of Bṛhaspati.
Purport: 

The ācāryas give various reasons why Lord Kṛṣṇa sent Uddhava to Vṛndāvana. The Lord had promised the residents of Vṛndāvana: āyāsye, “I shall return.” (Bhāg. 10.39.35) Also, in the previous chapter Lord Kṛṣṇa promised Nanda Mahārāja: draṣṭum eṣyāmaḥ, “We will come back to see you and mother Yaśodā.” (Bhāg. 10.45.23) At the same time, the Lord could not break His promise to Śrī Vasudeva and mother Devakī to finally spend some time with them after they had suffered for so many years. Therefore, the Lord decided to send His intimate representative to Vṛndāvana in His place.

The question may be asked, Why did Kṛṣṇa not invite Nanda and Yaśodā to visit Him in Mathurā? According to Śrīla Jīva Gosvāmī, for the Lord to have exchanged loving feelings with Nanda and Yaśodā in the same place and at the same time that He was exchanging them with Vasudeva and Devakī would have created an awkward situation in the Lord’s pastimes. Thus Kṛṣṇa did not invite Nanda and Yaśodā to stay with Him in Mathurā. The residents of Vṛndāvana had their own way of understanding Kṛṣṇa, and their feelings could not have been appropriately expressed on a regular basis in the kingly atmosphere of Mathurā.

Śrī Uddhava is described in this verse as buddhi-sattamaḥ, “the most intelligent,” and thus he could expertly pacify the residents of Vṛndāvana, who were feeling such intense separation from Lord Kṛṣṇa. Then, upon his return to Mathurā, Uddhava would describe to all the members of the Vṛṣṇi dynasty the extraordinary pure love he had seen in Vṛndāvana. Indeed, the love the cowherd men and gopīs felt for Kṛṣṇa was far beyond anything the Lord’s other devotees had ever experienced, and by hearing about that love all the Lord’s devotees would increase their faith and devotion.

As stated in the Third Canto by the Lord Himself, noddhavo ’nv api man-nyūnaḥ: “Uddhava is not even slightly different from Me.” Resembling Kṛṣṇa so much, Uddhava was the perfect person to carry out the Lord’s mission in Vṛndāvana. In fact, Śrī Hari-vaṁśa states that Uddhava is the son of Vasudeva’s brother Devabhāga: uddhavo devabhāgasya mahā-bhāgaḥ suto ’bhavat. In other words, he is a cousin-brother of Śrī Kṛṣṇa’s.