Poisson point process

#1
I came across this in a network model:

Distribute N points according to a homogeneous Poisson point process in a two-dimensional space of unit area.

No more info was given. Could somebody enlighten me on what this means? Usually I think of this as:
1) Generate the random variable N = n distributed as Poisson for a given lambda and area.
2) Generate n uniform points in that area.

But here N is fixed. What would be a procedure for the statement in bold text above?