nabla

The name nabla for the upside-down delta ∇ (aka an atled) comes from its shape: it is vaguely reminiscent of a harp, which is "nevel" in Hebrew. V and B being interchangeable under some western Semitic circumstances, the name nabla was given to the symbol.

∇ is merely a differential operator producing the partial derivatives in each variable. So for f:Rⁿ→X,

∇f = (∂/∂x₁,...,∂/∂x_n)f

More mathematically, nabla (∇, ∇ in HTML) is a 3D vector that is composed of the three partial derivatives, this means :
( ∂/∂x, ∂/∂y, ∂/∂z)
It can be used to represent a number of vector operations on scalar fields or vector fields.
For instance,

• grad F = ( ∂F/∂x, ∂F/∂y, ∂F/∂z) =( ∂/∂x, ∂/∂y, ∂/∂z)F=∇ F
  
• curl F= ∇ × F //not demonstrated because of the formatting limitations of E2
  
• div F=∂F_x/∂x,∂F_y/∂y,∂F_z/∂z =( ∂/∂x, ∂/∂y, ∂/∂z).(F_x,F_y,F_z)=∇ . F
  
• Δ F=( ∂²F/∂x², ∂²F/∂y², ∂²F/∂z²) = ( ∂/∂x, ∂/∂y, ∂/∂z).( ∂/∂x, ∂/∂y, ∂/∂z)F = div grad F= ∇²F.

That pretty much sums it up, two vector field, two scalar fields, two applied on scalar fields, two applied on vector fields.