Previews of tracks in Minecraft have been shortened to 30 seconds on this wiki in accordance with fair use rationale. "11" and "Magnetic Circuit" are exempt from this.
"Haggstrom" is a cheerful, bright, hopeful-sounding melody being played on a kalimba (perhaps with some other chime instruments as well, such as a celesta or a glockenspiel), with a plucked bass and occasional string chords. The melody rises in intensity and the string chords become more drawn out and layered as a piano and a harp are layered with the kalimba and some quiet woodwinds join in to harmonize with the chords. After the chords stop, the piano, layered with a muffled glockenspiel, quietly plays some more of the melody before stopping.
Warm, plucky, echoing synths (or possibly a muffled harp sound) quietly fade in, playing mechanically staccato chords. A harp begins to softly play over them and the plucked bass continues quietly as what sounds like a trumpet distantly echoes in the background, before a louder glockenspiel begins playing a sparse melody, with reverse chimes echoing the melody and echoing synths in the background playing light staccato chords. These sounds become surrounded by grand, sweeping synths and strings playing chords as a harp plays an accompaniment. The chords stop and all of the instruments slowly fade out, leaving just the plucky synths as the track ends.
"Haggstrom" is played in septuple time (precisely 7/4 time).
The Bandcamp page for "Haggstrom" is captioned with "MHG MHG MHG", likely referring to anosou, or Mattias Häggström Gerdt, who composed for other Mojang projects like Cobalt and Catacomb Snatch.