Spectral music is contemporary art music that makes use of the natural harmonic overtone series - think the nodes that appear in a vibrating string or column of air, if you've ever taken physics. This presentation was written from this point of view, even though this piece is not explicitly based on spectral techniques.
The notation can get a little hairy (furry? Furrer-y?), but essentially any set such as  is a way of classifying a group of four particular notes by their mutual distance on the staff. It's not dependent on explicit pitch; only relative pitch. Think of it as a more generalized way of talking about chords.
If you read farther, you'll see a Tetris slide. This analogy was made due to the repeated emergence of blocks of material (sets, as above) in the piano part that later are passed on to the violin. The continual emergence and repositioning of new blocks of material inspired the analogy.
Let's dive in. First, the recording from our class presentation. This is the last few minutes on the 8-minute piece, starting from rehearsal N, at the middle of page 7 of the score below: