Anguish is a term used in philosophy, often as a translation from the Latin for angst. It is a paramount feature of existentialist philosophy, in which anguish is often understood as the experience of an utterly free being in a world with zero absolutes (existential despair). In the theology of Kierkegaard, it refers to a being with total free will who is in a constant state of spiritual fear that his freedom will lead him to fall short of the standards that God has laid out for them.
Kierkegaard views anguish as the same as suffering. Everyone wants to find the "truth" but it takes anguish and suffering to "appropriate" the truth. Kierkegaard put it this way in 1847 and 1850.
All the knowledge allied with inquisitiveness, thirst for knowledge, natural talent, the self-seeking passion, all the knowledge the natural man promptly understands to be worth learning is also basically and essentially easy to learn, and aptitude is involved here from first to last. Therefore people are willing enough to learn when it is a matter of learning more, but when it is a matter of learning anew through sufferings, then learning becomes hard and heavy, then aptitude does not help, but on the other hand no one is excluded even though he is ever so lacking in aptitude. The lowliest, the simplest, the most forsaken human being, someone whom all teachers give up but heaven has by no means given up-he can learn obedience fully as well as anyone else.— Søren Kierkegaard, Upbuilding Discourses in Various Spirits, 1847, Hong translation, pp. 252–253
Is “truth” the sort of thing one might conceivably appropriate without more ado by means of another man? Without more ado-that is without being willing to be developed and tried, to fight and to suffer, just as he did who acquired the truth for himself? Is not that as impossible as to sleep or dream oneself into the truth. Is it not just as impossible to appropriate it thus without more ado however wide awake one might be? Or is one really wide awake, is not this a vain conceit, when one does not understand or will not understand that with respect to the truth there is no shortcut which dispenses with the necessity of acquiring it, and with that respect to acquire it from generation to generation there is no essential shortcut, so that every generation and every individual in the generation must essentially begin again from the start?— Søren Kierkegaard, Training in Christianity, 1850, pp. 181–182; Lowrie translation 1941, 2004
In the teachings of Sartre, anguish is seen when an utterly captured being realizes the unpredictability of his or her action. For example, when walking along a cliff, you would feel anguish to know that you have the freedom to throw yourself down to your imminent death.
The dictionary definition of anguish at Wiktionary