Nrisimha-chaturdasi is the divine appearance day of Nrisimhadeva, Lord Krishna’s man-lion incarnation, who removes all obstacles on the path of devotional service out of His great compassion. Narasimhadeva appeared at dusk on the Shukla Chaturdashi (fourteenth day of the bright fortnight) in the month of Vaishakha (May). Devotees fast till dusk on this day.

Srila Prabhupada writes (Bhagavatam 7.8.51, purport):
The Supreme Personality of Godhead in His transcendental form of Lord Nrisimhadeva is always ready to kill the demons who always create disturbances in the minds of honest devotees. To spread the Krishna consciousness movement, devotees have to face many dangers and impediments all over the world, but a faithful servant who preaches with great devotion to the Lord must know that Lord Nrisimhadeva is always his protector.
Srila Bhaktivinoda Thakura, in his Navadvipa-bhava-taranga, writes of the significance that worship of Lord Nrisimhadeva has for a Gaudiya Vaishnava:
Therefore, I pray to the feet of Lord Nrisimhadeva to purify my heart and give me the desire to serve Krishna. Weeping, I beg at the lotus feet of Nrisimha that I may worship Sri Sri Radha and Krishna at Navadvipa-dhama, free from all obstacles.