Q:

What does this notation mean?

What does the prime symbol above the note mean? I have not seen it before.
This is from Haydn's Variations in F minor

A:

It's a form of staccato called staccatissimo.
Normal dot over/under a note means staccato, where the note is shortened by about a quarter of its normal length.
Staccatissimo, is an 'extreme' version, where the note is shortened by about three-quarters of its length. In this piece, those notes are played and let go of immediately, pretty well, the first F actuallly being shorter in duration than the second.

A:

To add a caveat to Tim's answer: this marking should generally be taken with a grain of salt — or more like a rather large pinch of salt — in music written prior to the 20th century. Most such markings on scores of older music are putting forth a performance opinion of the editor, rather than anything that the composer specified — and some editors are better performers than others. Composers were inconsistent about what markings they used for staccato, although they usually used a dot and always, as far as I know, left the degree of "staccato-ness" up to the interpreter.
For example, in this one, you can have a look at this performance (your two-bar sample is played at 0:55, and can be seen in the last two measures of the third staff line):

You will notice that your two bars in this edition of the music here have a total of four ordinary staccato dots. That suggests that your wedges are an editor's opinion. Listening to Backhaus's performance, I get the idea he doesn't agree with that opinion, for I don't see any special degree of extremeness about the staccatos that he uses.
So, it's probably a good idea to approach any written score with a certain degree of skepticism. Beyond having the right notes, key and time signatures, and the like, finer degrees of detail should not be assumed to come from the composer. Look at different scores of the same music and form your own opinions.
In fact, I suggest that you consider your performances not as a recreation of a composer's ideas, but as a collaboration between you and the composer. So again, form your own opinions, and don't be too concerned with finding the intellectually correct way to play something. If something feels right, then play it that way.

