Fear is due to worrying about the future. A person in Krsna consciousness has no fear because by his activities he is sure to go back to the spiritual sky, back home, back to Godhead. Therefore his future is very bright. Others, however, do not know what their future holds; they have no knowledge of what the next life holds. So they are therefore in constant anxiety. If we want to get free from anxiety, then the best course is to understand Krsna and be situated always in Krsna consciousness. In that way we will be free from all fear. In the Srimad-Bhagavatam (11.2.37) it is stated, bhayam dvitiyabhinivesatah syat: fear is caused by our absorption in the illusory energy. But those who are free from the illusory energy, those who are confident that they are not the material body, that they are spiritual parts of the Supreme Personality of Godhead, and who are therefore engaged in the transcendental service of the Supreme Godhead, have nothing to fear. Their future is very bright. This fear is a condition of persons who are not in Krsna consciousness. Abhayam, fearlessness, is possible only for one in Krsna consciousness.
(From Srila Prabhupada's purport to Bg 10.4-5)