I received zip containing font in .afm format. Is this some sort of source-code of a font that can be converted TTF/OTF or so?
How can I actually read and use this file?
As the name implies, a .afm file contains the metrics (kerning, letterspacing, etc.) information for a font. It is a Postscript file, but is not the font itself, which would have the same name with a .pfa extension. You would need both in order to run a conversion utility. The exact nature of the files and the conversion utility you would need (.pfa and .afm are generally Linux files, ascii Postscript versions of what would be compiled to .pfb and .pfm binary on Windows, for example) depends on which platform you’re on.
In any case, without the actual font outline data, the .afm file does nothing.
I did find one free utility that claims to do the conversion. Perhaps some other folks here will know of others.