I was walking yesterday and stumbled upon this windowless construction:
As opposed to the view below, the side is now covered and has a huge sliding door on the second floor:
Does anyone know what this is?
It is a long going construction in the center of the city. I don't think it is going to be completed any time soon, and the site itself was cleared for construction some time in 1990s. That is, it's a sort of a abscess in the center of Kharkov, which is going to stay incomplete for years.
You have current links in bytebuster's answer, and maybe you are also interested in this topic on skyscrapercity.com which discusses this construction since 2012. They had nice renders back in time, however the original (or it was not the first version already) plans to complete first phase in 2014 was nothing but a joke.
As this sign says:
it will be "Nikolsky" trading and entertainment center (Ukr.: ТРЦ «Нікольський»).
Location: 2, Pushkin street (Ukr.: вул. Пушкінська, 2).
Here's its official site (caution, YouTube video auto-starts).
And here is its page on "Encyclopedia of New Buildings" (in Russian) with some pictures.