This recording is the 2nd movement of Beethoven's popular Sonata Pathetique Op. 13 No. 8. The second movement is Adagio cantabile. "Cantabile" indicates that this movement should be played like a song, or something that has a distinct melody that one could sing along with. This piece was composed in 1798 and published the following year.
You can read further commentary on this piece, including a dedicatory note by visiting this page of my piano blog.
This selection was recorded at my home on my studio upright piano.