This is Beethoven’s written description of the fourth movement of his Sixteenth String Quartet, which is usually translated as “the difficult resolution,” although the narrator remarks on the next page that it could also be read as “the weighty resolution.”
Here is a video of the Hagen Quartet playing the fourth movement of the Beethoven String Quartet in F Major, opus 135:
In music, “resolution” refers to the movement from a dissonant, or out-of-key chord or sound, back to the main note or chord of the musical work. Since Beethoven used variation techniques in the Sixteenth String Quartet, not typical in this form, he might also have been referring to the return of the piece to its original theme(s) at the conclusion, following its meander through variations on the theme.
Kundera takes the philosophical implication of the phrase -- difficulty experienced in coming to a decision or conclusion to a story -- and runs with it. There is also a description of the "true story" behind Beethoven's use of the phrase much later, in section 8 of Part Five, which is on pages 195-196 of this edition).