Any person who can understand the feelings of all persons and incidents in all places at all times is called all-cognizant.
A nice example of the all-cognizant quality of the Lord is described in Śrīmad-Bhāgavatam, First Canto, Fifteenth Chapter, verse 11, in connection with Durvāsā Muni's visit to the house of the Pāṇḍavas in the forest. Following a calculated plan, Duryodhana sent Durvāsā Muni and his ten thousand disciples to be guests of the Pāṇḍavas in the forest. Duryodhana arranged for Durvāsā and his men to reach the place of the Pāṇḍavas just when the Pāṇḍavas' lunchtime ended, so that the Pāṇḍavas would be caught without sufficient means to feed such a large number of guests. Knowing Duryodhana's plan, Kṛṣṇa came to the Pāṇḍavas and asked their wife, Draupadī, if there were any remnants of food which she could offer to Him. Draupadī offered Him a container in which there was only a little fragment of some vegetable preparation, and Kṛṣṇa at once ate it. At that moment all of the sages accompanying Durvāsā were taking bath in the river, and when Kṛṣṇa felt satisfaction from eating Draupadī's offering, they also felt satisfaction, and their hunger was gone. Because Durvāsā and his men were unable to eat anything more, they went away without coming into the house of the Pāṇḍavas. In this way the Pāṇḍavas were saved from the wrath of Durvāsā. Duryodhana had sent them because he knew that since the Pāṇḍavas would not be able to receive such a large number, Durvāsā would become angry, and the Pāṇḍavas would be cursed. But Kṛṣṇa saved them from this calamity by His trick and by His all-cognizant quality.