The Fourier number is a dimensionless number used in heat transfer calculations. It comes into play when studying conduction (heat transfer through solid objects) that varies over time, and when the lumped capacitance approach isn't appropriate. In (reasonably) plain English, it's a measure of how efficiently a given solid conducts or absorbs heat; something with a relatively large Fourier number conducts heat very effectively whereas something with a low Fourier number will soak up a lot of heat.
Using a more technical definition:
Fo = α t / Lc
where α is the thermal diffusivity (a property of the material), t is time, and Lc is the characteristic length of the object. In this case, the characteristic length is defined as the volume divided by the surface area.
From this definition, one can see that the Fourier number depends on both the material and the geometry of the object in question. The thermal diffusivity describes how effectively the material conducts heat: metals, for example, conduct heat very well; concrete doesn't. The characteristic length describes the geometry; two objects made out of the same material but with different ratios of volume to surface area will behave differently.
Node your homework - this writeup courtesy of my MAE336 exam on Monday.