Noise as generally referred to, is interpreted as acoustical noise.
This is what I take your question to be about, though there are other types e.g. electrical.
(Acoustical) Noise is a signal comprised of a relatively random mixture of wavelengths of sound.
Sound waves are longitudinal in nature and correspond to momentary changes in pressure within a medium such as air.
"Longitudinal" means that the wave motion is in the same direction as the overall motion of propagation of the wave (c.f. transverse)
Therefore one can generate a noise, from for instance a small "explosion", such as by clapping one's hands.
A pressure wave spreads outwards, with 1/r^2 diminuation. This transmitted pressure wave's oscillations are superimposed
on the random motion of the air molecules, which is due to heat.
The question therefore arises: why can't you hear heat? The answer is that the ear drum, though small relative to us, is large enough
in comparison to the molecules in the air vibrating due to their heat, for the random heat motion to be averaged/cancelled
 out over the ear drum, and hence undetected.
Some more facts about noise/sound:
Sounds are determined and measured by three factors: frequency, amplitude and (shape of) waveform.
Like other wave forms of energy, they are subject to refraction, reflection and interference.
It is primarily this refractive effect on sound, due to the varying viscosity of air, and speed of wind, with altitude, that causes sounds to 
travel better "with the wind".
The speed of sound depends on the density and elasticity of the medium, sound generally travels faster in denser media, such as
 solids and liquids, than in gases. Similarly, sounds travel slower with increasing altitude as our atmosphere thins.
The speed of propagation of sound at sea level in air is about 760mph.
 In the absence of any medium (e.g. in vacuo), sound cannot be propagated at all 
("In space noone can hear you scream!").
Soft materials generally absorb noise, while hard materials generally reflect it.
ln(perceived intensity of a sound) is proportional to 1/5 ln(actual power of the sound) - due to evolution of the human ear.

For more/more detailed info please consult an encyclopedia - search on the terms:
noise, sound, wave motion, oscillation, acoustics, interference, ear.