Neutral vs. Colored:
Colored sound is when certain frequencies are played back at higher or lower volumes than is natural according to the recording. Every headphone is colored to a degree, but headphones that are called "colored" do it to a greater degree. A lot of what you ask about is the result of coloration. Neutral is where everything is played back as the recording dictates. Headphones that are called "neutral" aren't colored to a great degree, and all of the frequencies are relatively balanced.
Forward vs. Laid Back:
Forward sound is caused by coloration that increases the volume of the "forward" frequencies. Bass, midrange, treble, or individual instruments which usually populate a certain part of these, can be forward. What happens is the louder frequencies appear closer than they should to the listener in the soundstage. Additionally, because of the increased volume small details in the frequencies are easier to distinguish, which also makes the instruments sound closer. It's "forward" because the listener feels closer to the musicians. A forward headphone usually emphasizes the upper midrange and treble, but like I said bass can be forward too. Laid back is the opposite. Frequencies are quieter and sound farther away.
Bright vs. Warm vs. Dark:
Generally speaking, bright sound is increased volume in the upper midrange and treble, and warm sound is increased volume in lower midrange and bass. Dark sound is usually warm sound, and characterized by quiet and "veiled" treble, where detail is hard to hear.
Dry:
Not totally sure, but I believe it would be characterized by a perceived lack of lower midrange, which makes things sound less warm and more analytical. Another symptom would probably be bright, harsh, and grainy treble.
PRaT:
Pace, Rhythm, and Timing. I'm not sure if there's a formal scientific definition, or if it's just a made-up audiophile concept to explain why they like an inferior and overpriced headphone. If I could characterize it I would say it relies on a punchy midbass, forward upper midrange, underdamped response, and fast decay.
I've never heard uptight, but it probably means about the same as dry and without any PRaT.