Quote from StarTrek.com:
Self-propelled missiles consisting of a small quantity of matter and antimatter bound together in a magnetic container, used as a tactical weapon by Federation starships.
Quote from memory-alpha:
The Making of Star Trek gave this description of the photon torpedo: "...photon torpedoes, which are energy pods of matter and anti-matter contained and held temporarily separated in a magno-photon force field. These can be used as torpedoes or depth charges, and can be set with electrochemical, proximity, and a variety of other fuses. Photon torpedoes can be fired directly at a target, laid out as a minefield, or scattered in an attacker's path as depth charges.
Photon torpedoes also have a detonator which can be activated remotely to abort the impact.
Photon torpedoes were different in color and use i the Star Trek series.
Quote from Wiki:
When fired, photon torpedoes usually appear as a spiky ball of energy of varying colours, such as red, orange, yellow, blue, or green.
TOS photon torpedoes look like this:
This can be called purple, or white if you will.
In the movie, photon torpedo were blue in color.
From the movie from 2009:
The earliest use of photon torpedoes by a Starfleet vessel however
occurred in Star Trek, when the USS Kelvin defended itself from
torpedoes fired by the Narada with phasers and photon torpedoes in a
scene set in the year 2233. The blue bolts were not identified in the
dialogue of the film, but were identified in the script as photons.
So they varied over the years, as some kind of globes of plasma or different energy. If I remember correctly, the Klingon photon torpedoes were green in color. The TNG, Voyager era torpedoes are reddish-orange in color.
I thought that it would be good to mention, that the sound of a photon torpedo was duplicated from an old movie.
The sound of photon torpedoes firing was that of the disintegration ray from the original The War of the Worlds.
The glow can be explained by the shields, surrounding the torpedoes. Also, every torpedo has a warp sustainer engine attached to it, which can further explain it's glow and color.
There is a theory that all photon torpedoes are black, and thus are hard to spot in the dark matter of space - which leaves the engine coils visible. Although debatable, this is probably not true, and I'll just leave it at that.
The color can also be due to the frequency of the shield at launch.
But, what is the real cause of the glow and color?
The photon torpedo consists of 1.5kg of antimatter and 1.5kg of (conventional) matter, which makes it 3kg of matter. It's coil is hot, which results in the glow effect. The hotter the coil the brighter the glow. It may explain some of it's color. The photon torpedo also emits gases (ex. deuterium gas), which cause some of the coloring. Depending on which structure is used, the color is formed.
Deuterium discharge tube (from real life):
One more effect of this is the radiation, which depends on the casing composition that stores all of this massive energy. This massive energy may be emitted by gamma rays and exotic particles. It reacts differently to various material reactions during the launch inside the casing, thus another way to impact the color.
The rotation can be explained as the rotation of any projectile.