What is NumberSequence.new and what do I use it for?

Number Sequences are types used to set a value on Transparency or Size for objects like Particle Emitters or Trails.

Depending on what you enter in the arguments of the paranthesis can make the Transparency or Size look different.

You could set the Transparency and Size to a ParticleEmitter like so in a script:

local emitter = Instance.new("ParticleEmitter")

--This would make the Transparency start at 0 and slowly turn invisible, at 1.
emitter.Transparency = NumberSequence.new(0, 1)

--This would make the size of the emitter to 5
emitter.Size = NumberSequence.new(5)

emitter.Parent = workspace.SomePart

You can even edit NumberSequences using the Properties window while a ParticleEmitter or Trail is selected.

Wiki Link It's used for Trails, Beams, and ParticleEmitters.