In a two dimensional curl what does the number you get represent? As for example let the field be $\mathbf{F} = \langle -y,x\rangle$.  When I do the math I get $2$!  But $2$ what ?   One source says it measure "twice the angular speed" because we are measuring unit angular speed" .  I assume $2$ is a number that applies to only this particular example... then what happens with other examples? Is it possible to have $4$,$5$, $6$ and is that then $4$,$5$, $6$ times the angular speed because we are measuring unit angular speed?  Any help is appreciated. I have also another example $G= <x,x>$and the Curl = $1$. 
Now if the curl represents a direction , let's assume this and we place it in the context of the $3$ dimensional curl then since the direction is perpendicular to the plane of the forces causing the spin, how can the spin be in the plane when the force is pointing up? 
 A: Actually, it's always twice (2 times) the angular velocity close to the point, in the sense that if you put a very tiny pinwheel/paddle/rudder/whatever at a point $(x,y)$ in a fluid flowing according to $\langle F_1,F_2\rangle$, then it will spin at counter-clockwise angular velocity equal to one half the scalar curl. To address your other question about the direction of the vector curl pointing up out of the plane, that represents the direction of rotation of the pinwheel via the right hand rule.
You can find a thorough explanation about this and more at these notes by professor emeritus Jeffery Cooper, but I personally prefer the diagram/explanation at this MathInsight page. I think this diagram from mathinsight is particularly useful for thinking about this: 

The scalar curl $(F_2)_x-(F_1)_y$ is approximately $\dfrac{F_2\text{(right)}-F_2\text{(left)}}{\text{diameter of circle}}-\dfrac{(F_1\text{(top)}-F_1\text{(bottom)})}{\text{diameter of circle}}$. 
In a straightforward case like $\langle-7y,7x\rangle$ at the origin (think a pinwheel of radius $1$), we'd have a counterclockwise rotation of angular speed $7$ (because of how radians are defined), but $\dfrac{F_2\text{(right)}-F_2\text{(left)}-F_1\text{(top)}+F_1\text{(bottom)}}{\text{diameter of circle}}=\dfrac{7-(-7)-(-7)+7}{2}=\dfrac{7\cdot4}{2}=2\cdot7$.
