Why do I sometimes see a backtick with a single quote `like this'? What's the name of this usage? What are some good references so I can find more information by myself?
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From the point of view of English usage, there is no difference other than appearance between the "backtick" (`) and the single quote mark ('). The characters exist in these forms because of compromises made in older computer character sets. Preceding computers, there is a long history in printing typography of using slightly different shapes for the opening and closing single quotes. In the more modern computer character set known as Unicode, there are new codes for these curved marks, the left (‘) and right (’) single quotes. Because of various problems with computers, a mix of all four single quote characters may be found, but should be considered equivalent (except for their visual appearance).
Basically, as answered by @mgkrebbs, quotations like 'this' or `this' are faulty typographic usage introduced with limited character sets, first with 19th century typewriters then with digital character encoding. The proper (Unicode) characters are ‘these’. The same happens with apostrophe and primes (for feet and inches). One should type
But it's easier said than done.
For reference about these various "apostrophes" I've found the following documents:
Of course, all this is mainly on English. Digressing further away from your question, you have other interesting things like the Mè'phàà language of Mexico, which uses the straight quote as a casing letter (pdf), with both a lower case ꞌ and an upper case Ꞌ version, both added in Unicode 5.1.