The story
Toska is Russian, and dictionaries split it into three senses: melancholy, boredom and longing. Russian speakers hear one feeling. The word goes back to Proto-Slavic *tъska and may be related to tiskat', 'to squeeze', which suits a feeling so often described as a weight on the chest. From it come toskovat', 'to pine', and the adjective tosklivyi, 'dreary'.
Vladimir Nabokov, in the commentary to his English translation of Eugene Onegin, wrote that no single English word renders all its shades. At its deepest, he said, it is spiritual anguish without a specific cause, and at its lightest it fades into ennui. In between sit a vague restlessness and a longing with nothing to long for.
That range is what makes it hard to translate. Melancholy is too calm, and yearning needs an object. Toska can be about a person or a place, or about nothing at all.
Chekhov wrote a short story called Toska in 1886, usually translated as Misery. A Petersburg cab driver whose son has just died spends the evening trying to tell someone, and nobody will listen. In the end he tells his horse.
A modern scene: a Sunday evening in late November, the light gone by four, a flat on the edge of a big city. Nothing is wrong. The kettle boils, the radiator ticks, and something in the chest will not settle. That is toska at its everyday setting.